SUPA. Quantum Many-Body Physics with Multimode Cavity QED. Jonathan Keeling FOUNDED. University of St Andrews

Transcription

1 Quantum Many-Body Physics with Multimode Cavity QED Jonathan Keeling University of St Andrews FOUNDED 113 SUPA CONDMAT17, Copenhagen, May 17 Jonathan Keeling Multimode cavity QED CONDMAT17 1

2 What can quantum systems do? Condensed matter physics: two types of question What physics is needed to explain the material properties we do see Jonathan Keeling Multimode cavity QED CONDMAT17

3 What can quantum systems do? Condensed matter physics: two types of question What physics is needed to explain the material properties we do see Jonathan Keeling Multimode cavity QED CONDMAT17

4 What can quantum systems do? Condensed matter physics: two types of question What physics is needed to explain the material properties we do see to What material properties can be possible from quantum physics? Jonathan Keeling Multimode cavity QED CONDMAT17

5 What can quantum systems do? Condensed matter physics: two types of question What physics is needed to explain the material properties we do see to What material properties can be possible from quantum physics? How? Doping, strain, heterostructure growth, nanofabrication... Jonathan Keeling Multimode cavity QED CONDMAT17

6 What can quantum systems do? Condensed matter physics: two types of question What physics is needed to explain the material properties we do see to What material properties can be possible from quantum physics? How? Doping, strain, heterostructure growth, nanofabrication... Floquet driving, strong matter-light coupling... Jonathan Keeling Multimode cavity QED CONDMAT17

7 From cavity QED... g Precision tests of quantum optics I I I Purcell effect, strong coupling Rabi oscillations, collapse & revival Resonant fluoresecence, EIT Many body cavity QED? I Phase transitions: Lasing, superfluoresence, superradiance Jonathan Keeling Multimode cavity QED CONDMAT17 3

8 From cavity QED... g Precision tests of quantum optics I I I Purcell effect, strong coupling Rabi oscillations, collapse & revival Resonant fluoresecence, EIT Many body cavity QED? I Phase transitions: Lasing, superfluoresence, superradiance Jonathan Keeling Multimode cavity QED CONDMAT17 3

9 From cavity QED... g Precision tests of quantum optics I I I Purcell effect, strong coupling Rabi oscillations, collapse & revival Resonant fluoresecence, EIT Many body cavity QED? [Circuit QED array, Houck group ] I Phase transitions: Lasing, superfluoresence, superradiance Jonathan Keeling Multimode cavity QED CONDMAT17 3

10 ... synthetic cavity QED: Raman driving Tunable coupling via Raman Ω Cavity Ω H eff =... Ωg ( σ + n a + H.c. ) Ω ω level system Real systems: loss t ρ = i[h, ρ] + κl[a, ρ] +... To balance loss, counter-rotating: H eff =... Ωg σx n(a + a ) [Dimer et al. PRA 7] Jonathan Keeling Multimode cavity QED CONDMAT17

11 ... synthetic cavity QED: Raman driving Tunable coupling via Raman Ω Cavity Ω H eff =... Ωg ( σ + n a + H.c. ) Ω ω level system Real systems: loss t ρ = i[h, ρ] + κl[a, ρ] +... To balance loss, counter-rotating: Ω Cavity Ω H eff =... Ωg σx n(a + a ) ω level system [Dimer et al. PRA 7] Jonathan Keeling Multimode cavity QED CONDMAT17

12 (Multimode) cavity QED H = k ω k a k a k + n ω σ + n σ n + n,k g k,n (a k + a k )(σ+ n + σ n ) ρ = i[h, ρ] + κ k L[a k, ρ] + γ i L[σ n, ρ] Compare g (or g N) vs: κ, γ ωk, ω Jonathan Keeling Multimode cavity QED CONDMAT17 5

13 (Multimode) cavity QED H = k ω k a k a k + n ω σ + n σ n + n,k g k,n (a k + a k )(σ+ n + σ n ) ρ = i[h, ρ] + κ k L[a k, ρ] + γ i L[σ n, ρ] Compare g (or g N) vs: κ, γ ωk, ω ωk, ω Jonathan Keeling Multimode cavity QED CONDMAT17 5

14 (Multimode) cavity QED H = k ω k a k a k + n ω σ + n σ n + n,k g k,n (a k + a k )(σ+ n + σ n ) ρ = i[h, ρ] + κ k L[a k, ρ] + γ i L[σ n, ρ] Compare g (or g N) vs: κ, γ bandwidth ωk, ω Jonathan Keeling Multimode cavity QED CONDMAT17 5

15 Multimode cavities Confocal cavity L = R: Modes Ξ l,m (r) = H l (x)h m (y), l + m fixed parity Tune between degenerate vs non-degenerate Jonathan Keeling Multimode cavity QED CONDMAT17

16 Multimode cavities Confocal cavity L = R: Modes Ξ l,m (r) = H l (x)h m (y), l + m fixed parity Tune between degenerate vs non-degenerate Jonathan Keeling Multimode cavity QED CONDMAT17

17 1 Introduction: Tunable multimode Cavity QED Density wave polaritons Superradiance transition Supermode density wave polariton condensation 3 Spin wave polaritons Effects of loss Spin glass Meissner-like effect Jonathan Keeling Multimode cavity QED CONDMAT17 7

18 Mapping transverse pumping to Dicke model κ κ g ψ z Ω x Pump Level System Atomic states: ψ(r) = ψ + ψ cos(qx) cos(qz) H eff = (ω c ω P ) a a + }{{} n c ω σz n + Ωg x σ }{{} n(a + a ) g eff Extra feedback term U, cavity loss κ Z symmetry: phase of light Jonathan Keeling Multimode cavity QED CONDMAT17 8

19 Mapping transverse pumping to Dicke model z κ κ gψ Ω x Pump Level System Atomic states: ψ(r) = ψ + ψ cos(qx) cos(qz) H eff = (ω c ω P ) a a + }{{} n c ω σz n + Ωg }{{} g eff x σ Extra feedback term U, cavity loss κ Z symmetry: phase of light n(a + a ) g σ }{{ na z a } U Jonathan Keeling Multimode cavity QED CONDMAT17 8

20 Mapping transverse pumping to Dicke model z κ κ gψ Ω x Pump Level System Atomic states: ψ(r) = ψ + ψ cos(qx) cos(qz) H eff = (ω c ω P ) a a + }{{} n c ω σz n + Ωg }{{} g eff x σ Extra feedback term U, cavity loss κ Z symmetry: phase of light n(a + a ) g σ }{{ na z a } U Atoms: vs Jonathan Keeling Multimode cavity QED CONDMAT17 8

21 Classical dynamics Changing U: U = U < U > UN= SR ω (MHz) - SR g N (MHz) [JK et al. PRL 1, Bhaseen et al. PRA 1] Jonathan Keeling Multimode cavity QED CONDMAT17 9

22 Classical dynamics Changing U: U = U < U > gψ Ω U g ω c ω a Level System UN=- SRA ω (MHz) + SRB - SRA g N (MHz) [JK et al. PRL 1, Bhaseen et al. PRA 1] Jonathan Keeling Multimode cavity QED CONDMAT17 9

23 Classical dynamics Changing U: U = U < U > g ψ Ω U g ω c ω a Level System UN= SRA ω (MHz) - SRA g N (MHz) [JK et al. PRL 1, Bhaseen et al. PRA 1] Jonathan Keeling Multimode cavity QED CONDMAT17 9

24 Classical dynamics Changing U: U = U < U > g ψ Ω U g ω c ω a Level System ω (MHz) UN= Persistent Oscillations g N (MHz) SRA SRA [JK et al. PRL 1, Bhaseen et al. PRA 1] ψ t (ms) Jonathan Keeling Multimode cavity QED CONDMAT17 9

25 Single mode experiments Pump laser Bragg planes Ritsch et al. PRL Figure 1 Simulated stationary distribution of 1, high-field-seeking atoms in an optical resonator transversely illuminated by laser light. The atoms self-order in a crystalline structure with Bragg planes (dashed diagonal lines as a guide to the eye) maximizing the coherent scattering into the resonator mode as predicted and observed in refs 1 and. analogous to Brazovskii s transition where a uniform spatial distribution abruptly of the nucleation of new atomic quantum phases 5. Thus, real-time non-destructive monitoring of the dynamics of a quantum phase transition can be foreseen. As cavity quantum electrodynamics (QED) set-ups with single particles coupled to super-mirror resonators pose severe experimental challenges, theoretical considerations invoking degenerate quantum gases were long considered to be thought experiments only. However, using the recent exciting developments in the optical manipulation of ultracold gases, several teams have now implemented cavity- QED systems involving Bose Einstein condensates and super mirrors. Up to a million atoms at close to T = can be trapped in the field of a few photons (or even a single one),7. These experiments enter the strong-coupling regime where coherent quantum coupling dominates dissipation by more than three orders of magnitude. Here, the optical potentials and thus the light forces have genuine quantum properties so that the light and the particles become dynamically entangled. As a consequence, the dynamics can lead to superpositions of light-field states associated Jonathan Keeling Multimode cavity QED CONDMAT17 1

26 time phase of the Bragg-scattered intracavity light. Moreover, we observe collectively enhanced friction of the nucleation of new atomic quantum forces Single damping themode center-of-mass experiments (c.m.) motion of two-level Cs atoms at peak decelerations of 1 3 m=s phases 5. Thus, real-time non-destructive and light-atom detunings up to GHz. Bragg Because planes the monitoring of the dynamics of a quantum collective damping force is present even on an open transition and in the weak-coupling regime, we anticipate phase transition can be foreseen. the possibility of slowing samples of other polarizable As cavity quantum electrodynamics particles. (QED) set-ups with single particles The experimental apparatus [Fig. 1(a)] and procedure are similar to those described in Ref. [1]. A nearly coupled to super-mirror resonators pose confocal optical resonator with finesse F 1 and severe experimental challenges, theoretical length L 7:5 cm is oriented along the vertical z axis. considerations invoking degenerate The cavity has a free spectral range of c=l GHz and a multimode transmission spectrum width of quantum gases were long considered to be about MHz [1]. A retroreflected laser beam along thought experiments only. However, using the horizontal x axis with waist size w Pump laser mm intersects the cavity center. This y-polarized pump beam, the recent exciting developments in the tuned near the cesium D transition wavelength optical manipulation of ultracold gases, =k 85 nm, is derived from a tunable diode laser several teams have now implemented cavityand amplified to a power of 1 mw in a semiconductor tapered amplifier, yielding single-beam intensities up to QED systems involving Bose Einstein I=I Ritsch s : et 1 al. PRL 3, where I s 1:1 mw=cm is the D line condensates and super mirrors. Up to Thermal Figure 1 Simulated atoms, stationary momentum distribution of PHYSICAL state a REmillion VIEW LETatoms TERS week ending VOLUME 91, NUMBER at close 1to NOVEMBER T = 3 can be 1, high-field-seeking atoms (a) in an optical trapped.5in the field φ = of a few photons (or resonator transversely illuminated by laser light. even a single one),7 λ (a) (b) P F ' φ = π 3/ 1 δ e. φ =. π/ a These z experiments The atoms self-order Emitted in Light a crystalline structure with enter the.3 Pump Beams strong-coupling regime where ω Bragg planes (dashed diagonal lines as i x λ (b) π a guide to. coherent quantum coupling dominates Z F the eye) maximizing the coherent scattering g = φ into.1 S 1/ dissipation by more than three orders of the Cavity resonator Mirrors mode as X predicted and observed F g =3 in 1 3 magnitude. 1 Here, the optical 1 potentials refs 1 and. Time (ms) Pulse Separation Time T FIG. 1. (a) Schematic experimental setup. Atoms falling and thus the light forces off (µs) have genuine FIG.. Simultaneous time traces of the intracavity FIG. 3. The fraction of pulse pairs with relative phase shift along the cavity axis are illuminated intensity (a) by(arbitrary horizontal units) andpump field phase (b). The parameters are (MIT) quantum is plotted properties versus pulse separation so time. that The solid the circles, light and the beams Vuletic and self-organize et al. PRL into a density 3 grating, N 8: emitting 1, a= into 1:59 GHz, c= open circles, and solid squares correspond to =1, MHz, and I=I s. particles =1, become and = =1, dynamically respectively. The parametersentangled. are the cavity. (b) Cs D line. The atom approximates an open twolevel analogous system F g to! Brazovskii s Fe the same as for Fig., except here N 1:3 1 since the For short light-atom transition T off, the detuning relative phase where is is predominantly As a consequence, the dynamics 7. The inset shows the two possible lattice configurations producing relative can lead to phase shift in the emitted light. much greater than the excited state hyperfine. AsTsplitting. a uniform spatial distribution off increases, relative phases of Jonathan Keeling abruptly Multimode superpositions cavity QED of light-field states associated CONDMAT17 1 Emission appear, and the difference f f decays with a time Fraction of Pulse Pairs

27 time phase of the Bragg-scattered intracavity light. Moreover, we observe collectively enhanced friction of the nucleation of new atomic quantum forces Single damping themode center-of-mass experiments (c.m.) motion of two-level Cs atoms at peak decelerations of 1 3 m=s phases 5. Thus, real-time non-destructive and light-atom detunings up to GHz. Bragg Because planes the monitoring of the dynamics of a quantum collective damping force is present even on an open transition and in the weak-coupling regime, we anticipate phase transition can be foreseen. the possibility of slowing samples of other polarizable As BEC, cavity quantum momentum electrodynamics state particles. (QED) set-ups with single particles The experimental apparatus [Fig. 1(a)] and procedure are similar to those described in Ref. [1]. A nearly coupled to super-mirror resonators pose confocal optical resonator with finesse F 1 and severe experimental challenges, theoretical length L 7:5 cm is oriented along the vertical z axis. considerations invoking degenerate The cavity has a free spectral range of c=l GHz and a multimode transmission spectrum width of quantum gases were long considered to be about MHz [1]. A retroreflected laser beam along thought experiments only. However, using the horizontal x axis with waist size w Pump laser mm intersects the cavity center. This y-polarized pump beam, the recent exciting developments in the tuned near the cesium D transition wavelength optical manipulation of ultracold gases, =k 85 nm, is derived from a tunable diode laser several teams have now implemented cavityand amplified to a power of 1 mw in a semiconductor tapered amplifier, yielding single-beam intensities up to QED systems involving Bose Einstein I=I Ritsch s : et 1 al. PRL 3, where I s 1:1 mw=cm is the D line condensates and super mirrors. Up to Thermal Figure 1 Simulated atoms, stationary momentum distribution of PHYSICAL state a REmillion VIEW LETatoms TERS week ending VOLUME 91, NUMBER at close 1to NOVEMBER T = 3 can be 1, high-field-seeking atoms (a) in an optical trapped.5in the field φ = of a few photons (or resonator transversely illuminated by laser light. even a single one),7 λ (a) (b) P F ' φ = π 3/ 1 δ e. φ =. π/ a Baumann et al. These znature experiments 1 (ETH) The atoms self-order Emitted in Light a crystalline structure with enter the.3 Pump Beams strong-coupling regime where ω Bragg planes (dashed diagonal lines as i x λ (b) a guide to coherent Kinder π. quantum et al. coupling PRL 15 dominates (Hamburg) Z F the eye) maximizing the coherent scattering g = φ into.1 S 1/ dissipation by more than three orders of the Cavity resonator Mirrors mode as X predicted and observed F g =3 in 1 3 magnitude. 1 Here, the optical 1 potentials refs 1 and. Time (ms) Pulse Separation Time T FIG. 1. (a) Schematic experimental setup. Atoms falling and thus the light forces off (µs) have genuine FIG.. Simultaneous time traces of the intracavity FIG. 3. The fraction of pulse pairs with relative phase shift along the cavity axis are illuminated intensity (a) by(arbitrary horizontal units) andpump field phase (b). The parameters are (MIT) quantum is plotted properties versus pulse separation so time. that The solid the circles, light and the beams Vuletic and self-organize et al. PRL into a density 3 grating, N 8: emitting 1, a= into 1:59 GHz, c= open circles, and solid squares correspond to =1, MHz, and I=I s. particles =1, become and = =1, dynamically respectively. The parametersentangled. are the cavity. (b) Cs D line. The atom approximates an open twolevel analogous system F g to! Brazovskii s Fe the same as for Fig., except here N 1:3 1 since the For short light-atom transition T off, the detuning relative phase where is is predominantly As a consequence, the dynamics 7. The inset shows the two possible lattice configurations producing relative can lead to phase shift in the emitted light. much greater than the excited state hyperfine. AsTsplitting. a uniform spatial distribution off increases, relative phases of Jonathan Keeling abruptly Multimode superpositions cavity QED of light-field states associated CONDMAT17 1 Emission appear, and the difference f f decays with a time Fraction of Pulse Pairs

28 time phase of the Bragg-scattered intracavity light. Moreover, we observe collectively enhanced friction of the nucleation of new atomic quantum forces Single damping themode center-of-mass experiments (c.m.) motion of two-level Cs atoms at peak decelerations of 1 3 m=s phases 5. Thus, real-time non-destructive and light-atom detunings up to GHz. Bragg Because planes the monitoring of the dynamics of a quantum collective damping force is present even on an open transition and in the weak-coupling regime, we anticipate phase transition can be foreseen. the possibility of slowing samples of other polarizable As BEC, cavity quantum momentum electrodynamics state particles. (QED) set-ups with single particles The experimental apparatus [Fig. 1(a)] and procedure are similar to those described in Ref. [1]. A nearly coupled to super-mirror resonators pose confocal optical resonator with finesse F 1 and severe experimental challenges, theoretical length L 7:5 cm is oriented along the vertical z axis. considerations invoking degenerate The cavity has a free spectral range of c=l GHz and a multimode transmission spectrum width of quantum gases were long considered to be about MHz [1]. A retroreflected laser beam along thought experiments only. However, using the horizontal x axis with waist size w Pump laser mm intersects the cavity center. This y-polarized pump beam, the recent exciting developments in the tuned near the cesium D transition wavelength optical manipulation of ultracold gases, =k 85 nm, is derived from a tunable diode laser several teams have now implemented cavityand amplified to a power of 1 mw in a semiconductor tapered amplifier, yielding single-beam intensities up to QED systems involving Bose Einstein I=I Ritsch s : et 1 al. PRL 3, where I s 1:1 mw=cm is the D line condensates and super mirrors. Up to Thermal Figure 1 Simulated atoms, stationary momentum distribution of PHYSICAL state a REmillion VIEW LETatoms TERS week ending VOLUME 91, NUMBER at close 1to NOVEMBER T = 3 can be 1, high-field-seeking atoms (a) in an optical trapped.5in the field φ = of a few photons (or resonator transversely illuminated by laser light. even a single one),7 λ (a) (b) P F ' φ = π 3/ 1 δ e. φ =. π/ a Baumann et al. These znature experiments 1 (ETH) The atoms self-order Emitted in Light a crystalline structure with enter the.3 Pump Beams strong-coupling regime where ω Bragg planes (dashed diagonal lines as i x λ (b) a guide to coherent Kinder π. quantum et al. coupling PRL 15 dominates (Hamburg) Z F the eye) maximizing the coherent scattering g = φ into.1 S 1/ dissipation BEC, by hyperfine more than three states orders of the Cavity resonator Mirrors mode as X predicted and observed F g =3 in 1 3 magnitude. 1 Here, the optical 1 potentials refs 1 and. Time (ms) FIG. 1. (a) Schematic experimental setup. Atoms falling and thus BadenPulse the light etseparation al. forces PRL Time T off have 1 (µs) genuine (Singapore) FIG.. Simultaneous time traces of the intracavity FIG. 3. The fraction of pulse pairs with relative phase shift along the cavity axis are illuminated intensity (a) by(arbitrary horizontal units) andpump field phase (b). The parameters are (MIT) quantum is plotted properties versus pulse separation so time. that The solid the circles, light and the beams Vuletic and self-organize et al. PRL into a density 3 grating, N 8: emitting 1, a= into 1:59 GHz, c= open circles, and solid squares correspond to =1, MHz, and I=I s. particles =1, become and = =1, dynamically respectively. The parametersentangled. are the cavity. (b) Cs D line. The atom approximates an open twolevel analogous system F g to! Brazovskii s Fe the same as for Fig., except here N 1:3 1 since the For short light-atom transition T off, the detuning relative phase where is is predominantly As a consequence, the dynamics 7. The inset shows the two possible lattice configurations producing relative can lead to phase shift in the emitted light. much greater than the excited state hyperfine. AsTsplitting. a uniform spatial distribution off increases, relative phases of Jonathan Keeling abruptly Multimode superpositions cavity QED of light-field states associated CONDMAT17 1 Emission appear, and the difference f f decays with a time Fraction of Pulse Pairs

29 Density wave polaritons 1 Introduction: Tunable multimode Cavity QED Density wave polaritons Superradiance transition Supermode density wave polariton condensation 3 Spin wave polaritons Effects of loss Spin glass Meissner-like effect Jonathan Keeling Multimode cavity QED CONDMAT17 11

30 Superradiance in multimode cavity: Even family Jonathan Keeling Multimode cavity QED CONDMAT17 1

31 Superradiance in multimode cavity: Even family Jonathan Keeling Multimode cavity QED CONDMAT17 1

32 Superradiance in multimode cavity: Even family Jonathan Keeling Multimode cavity QED CONDMAT17 1

33 Superradiance in multimode cavity: Odd family Atomic time-of-flight structure factor ψ(r) = ψ (r) + ψ (r) cos(qx) cos(qz) Dependence on cloud position a 1 3 y b 1 3 y x 1 x Near-degeneracy of (1, ), (, 1) modes broken by matter-light coupling. Jonathan Keeling Multimode cavity QED CONDMAT17 13

34 Superradiance in multimode cavity: Odd family Atomic time-of-flight structure factor ψ(r) = ψ (r) + ψ (r) cos(qx) cos(qz) Dependence on cloud position a 1 3 y b 1 3 y x 1 x Near-degeneracy of (1, ), (, 1) modes broken by matter-light coupling. Jonathan Keeling Multimode cavity QED CONDMAT17 13

35 Superradiance in multimode cavity: Odd family Atomic time-of-flight structure factor ψ(r) = ψ (r) + ψ (r) cos(qx) cos(qz) Dependence on cloud position a 1 3 y b 1 3 y x 1 x Near-degeneracy of (1, ), (, 1) modes broken by matter-light coupling. Jonathan Keeling Multimode cavity QED CONDMAT17 13

36 Superradiance in multimode cavity: Odd family Atomic time-of-flight structure factor ψ(r) = ψ (r) + ψ (r) cos(qx) cos(qz) Dependence on cloud position a 1 3 y b 1 3 y x 1 x Near-degeneracy of (1, ), (, 1) modes broken by matter-light coupling. Jonathan Keeling Multimode cavity QED CONDMAT17 13

37 Synthetic cqed Possibilities Single mode vs multimode Momentum state vs hyperfine state XY vs Ising Thermal gas vs BEC vs disorder localised Jonathan Keeling Multimode cavity QED CONDMAT17 1

38 F F F Synthetic cqed Possibilities Single mode vs multimode QUANTUM OPTICS Crystals of atoms and light Helmut Ritsch ust as matter is used to control the propagation of light waves, light can Jbe used to manipulate matter waves. In typical situations, such as when light is guided by lenses or mirrors or when particles are trapped by optical tweezers and laser cooling, only one of the two effects is significant. Momentum state vs hyperfine state XY vs Ising However, confining a cold gas in a high-finesse optical resonator creates an unusual situation in which particles and photons dynamically influence each other s motion by momentum exchange on an equal footing. The particles create a dynamic refractive index that diffracts the light waves. These interfere and form structured optical potentials that guide the particles motion. In the simple generic case of high-field-seeking atoms in between two plane mirrors, one finds a well-defined threshold illumination intensity above which the particles order in a regular crystalline structure. They form ordered patterns with Bragg planes, which optimally couple the pump laser into the resonator 1. This maximizes the resonator field and thus minimizes the potential energy of particles trapped around local field maxima. The scaling of this phase-stable super-radiant scattering with the square of the particle number has been observed experimentally, and is a clear signature of such self-ordering. Sarang Gopalakrishnan and colleagues, reporting on page 85 of this issue 3, generalize the description of these complex coupled nonlinear dynamics by considering ultracold quantum gases in a multimode optical resonator. Here, photons and atoms can dynamically occupy a large number of modes. Using a functionalintegral formalism adapted from quantum field theory, Gopalakrishnan et al. are able to derive an effective atom-only action from which they uncover a wealth of new phenomena in this generalized configuration. One important result is that the phase transition to a crystal arrangement is first order and persists down to zero temperature. This represents a genuine quantum phase transition that involves Thermal gas vs BEC vs disorder localised analogous to Brazovskii s transition where a uniform spatial distribution abruptly transforms into a stripe pattern. This phase transition at zero temperature is solely driven by quantum fluctuations of the particle fields, which are dynamically amplified and develop into macroscopic spatial-density variations. (This resembles the way that large-scale structures are supposed to have appeared from quantum noise in the early Universe.) The spatial correlations and the form of the emerging structures are determined by the wavevectors supported by the optical-resonator geometry. With the help of extra confinement potentials for the particles that are introduced by light sheets, the dimensions of the emerging patterns can be externally controlled. Models with several interacting layered planes can be implemented. As an extra bonus, the set-up includes a built-in non-destructive monitoring system by virtue of analysis of the scattered light fields. In particular, at near-zero temperature news & views Cold atoms and photons confined together in high-quality optical resonators self-organize into complicated crystalline structures that have an optical-wavelength scale. Complex solid-state phenomena can be studied in real time on directly observable scales. Pump laser Bragg planes Figure 1 Simulated stationary distribution of 1, high-field-seeking atoms in an optical resonator transversely illuminated by laser light. The atoms self-order in a crystalline structure with Bragg planes (dashed diagonal lines as a guide to the eye) maximizing the coherent scattering into the resonator mode as predicted and observed in refs 1 and. of the nucleation of new atomic quantum phases 5. Thus, real-time non-destructive monitoring of the dynamics of a quantum phase transition can be foreseen. As cavity quantum electrodynamics (QED) set-ups with single particles coupled to super-mirror resonators pose severe experimental σ challenges, theoretical considerations invoking degenerate quantum σ + gases were long considered to be thought experiments only. However, using the recent exciting developments m =+1 in the optical manipulation m = of ultracold gases, m several = 1 teams have now implemented cavity- QED systems involving Bose Einstein condensates and super mirrors. Up to a million atoms at close to T = can be trapped in the field of a few photons (or even a single one),7. These experiments enter the strong-coupling regime where coherent quantum coupling dominates dissipation by more than three orders of magnitude. Here, the optical potentials and thus the light forces have genuine quantum properties so that the light and the particles become dynamically entangled. As a consequence, the dynamics can lead to superpositions of light-field states associated with different atomic quantum phases as an exotic form of a Schrödinger-cat state. The strong coherent coupling of atoms and photons can also be used as a controllable prototype interface of photonic- and atombased quantum computing. Whereas ultracold atoms interact directly only at close distances, the modification of the light field induced by a single particle influences the optical potential for virtually all other particles in the system 8. This longrange interaction can be tailored through the mirror geometry, and acts in a similar way to acoustic phonons in solid crystals. This adds an extra dimension to optical-lattice physics with ultracold quantum gases, which is already one of the most fruitful areas at the boundary of atomic and solid-state physics 9, including the physics of phonons, polarons or momentum-space pairing of particles. The tremendous recent progress has now surpassed the limits in readily Jonathan Keeling Multimode cavity QED CONDMAT17 1

39 F F F Synthetic cqed Possibilities Single mode vs multimode QUANTUM OPTICS Crystals of atoms and light Helmut Ritsch ust as matter is used to control the propagation of light waves, light can Jbe used to manipulate matter waves. In typical situations, such as when light is guided by lenses or mirrors or when particles are trapped by optical tweezers and laser cooling, only one of the two effects is significant. Momentum state vs hyperfine state XY vs Ising Cavity ω level system Ω However, confining a cold gas in a high-finesse optical resonator creates an unusual situation in which particles and photons dynamically influence each other s motion by momentum exchange on an equal footing. The particles create a dynamic refractive index that diffracts the light waves. These interfere and form structured optical potentials that guide the particles motion. In the simple generic case of high-field-seeking atoms in Cavity between two plane mirrors, one finds a well-defined threshold illumination intensity above which the particles order in Ω Ω a regular crystalline structure. They form ordered patterns with Bragg planes, which optimally couple the pump laser into the resonator 1. This ω maximizes the resonator field and thus minimizes the potential level system energy of particles trapped around local field maxima. The scaling of this phase-stable super-radiant scattering with the square of the particle number has been observed experimentally, and is a clear signature of such self-ordering. Sarang Gopalakrishnan and colleagues, reporting on page 85 of this issue 3, generalize the description of these complex coupled nonlinear dynamics by considering ultracold quantum gases in a multimode optical resonator. Here, photons and atoms can dynamically occupy a large number of modes. Using a functionalintegral formalism adapted from quantum field theory, Gopalakrishnan et al. are able to derive an effective atom-only action from which they uncover a wealth of new phenomena in this generalized configuration. One important result is that the phase transition to a crystal arrangement is first order and persists down to zero temperature. This represents a genuine quantum phase transition that involves Thermal gas vs BEC vs disorder localised analogous to Brazovskii s transition where a uniform spatial distribution abruptly transforms into a stripe pattern. This phase transition at zero temperature is solely driven by quantum fluctuations of the particle fields, which are dynamically amplified and develop into macroscopic spatial-density variations. (This resembles the way that large-scale structures are supposed to have appeared from quantum noise in the early Universe.) The spatial correlations and the form of the emerging structures are determined by the wavevectors supported by the optical-resonator geometry. With the help of extra confinement potentials for the particles that are introduced by light sheets, the dimensions of the emerging patterns can be externally controlled. Models with several interacting layered planes can be implemented. As an extra bonus, the set-up includes a built-in non-destructive monitoring system by virtue of analysis of the scattered light fields. In particular, at near-zero temperature news & views Cold atoms and photons confined together in high-quality optical resonators self-organize into complicated crystalline structures that have an optical-wavelength scale. Complex solid-state phenomena can be studied in real time on directly observable scales. Pump laser Bragg planes Figure 1 Simulated stationary distribution of 1, high-field-seeking atoms in an optical resonator transversely illuminated by laser light. The atoms self-order in a crystalline structure with Bragg planes (dashed diagonal lines as a guide to the eye) maximizing the coherent scattering into the resonator mode as predicted and observed in refs 1 and. of the nucleation of new atomic quantum phases 5. Thus, real-time non-destructive monitoring of the dynamics of a quantum phase transition can be foreseen. As cavity quantum electrodynamics (QED) set-ups with single particles coupled to super-mirror resonators pose severe experimental σ challenges, theoretical considerations invoking degenerate quantum σ + gases were long considered to be thought experiments only. However, using the recent exciting developments m =+1 in the optical manipulation m = of ultracold gases, m several = 1 teams have now implemented cavity- QED systems involving Bose Einstein condensates and super mirrors. Up to a million atoms at close to T = can be trapped in the field of a few photons (or even a single one),7. These experiments enter the strong-coupling regime where coherent quantum coupling dominates dissipation by more than three orders of magnitude. Here, the optical potentials and thus the light forces have genuine quantum properties so that the light and the particles become dynamically entangled. As a consequence, the dynamics can lead to superpositions of light-field states associated with different atomic quantum phases as an exotic form of a Schrödinger-cat state. The strong coherent coupling of atoms and photons can also be used as a controllable prototype interface of photonic- and atombased quantum computing. Whereas ultracold atoms interact directly only at close distances, the modification of the light field induced by a single particle influences the optical potential for virtually all other particles in the system 8. This longrange interaction can be tailored through the mirror geometry, and acts in a similar way to acoustic phonons in solid crystals. This adds an extra dimension to optical-lattice physics with ultracold quantum gases, which is already one of the most fruitful areas at the boundary of atomic and solid-state physics 9, including the physics of phonons, polarons or momentum-space pairing of particles. The tremendous recent progress has now surpassed the limits in readily Jonathan Keeling Multimode cavity QED CONDMAT17 1

40 F F F Synthetic cqed Possibilities Single mode vs multimode QUANTUM OPTICS Crystals of atoms and light Helmut Ritsch ust as matter is used to control the propagation of light waves, light can Jbe used to manipulate matter waves. In typical situations, such as when light is guided by lenses or mirrors or when particles are trapped by optical tweezers and laser cooling, only one of the two effects is significant. Momentum state vs hyperfine state XY vs Ising Cavity ω level system Ω However, confining a cold gas in a high-finesse optical resonator creates an unusual situation in which particles and photons dynamically influence each other s motion by momentum exchange on an equal footing. The particles create a dynamic refractive index that diffracts the light waves. These interfere and form structured optical potentials that guide the particles motion. In the simple generic case of high-field-seeking atoms in Cavity between two plane mirrors, one finds a well-defined threshold illumination intensity above which the particles order in Ω Ω a regular crystalline structure. They form ordered patterns with Bragg planes, which optimally couple the pump laser into the resonator 1. This ω maximizes the resonator field and thus minimizes the potential level system energy of particles trapped around local field maxima. The scaling of this phase-stable super-radiant scattering with the square of the particle number has been observed experimentally, and is a clear signature of such self-ordering. Sarang Gopalakrishnan and colleagues, reporting on page 85 of this issue 3, generalize the description of these complex coupled nonlinear dynamics by considering ultracold quantum gases in a multimode optical resonator. Here, photons and atoms can dynamically occupy a large number of modes. Using a functionalintegral formalism adapted from quantum field theory, Gopalakrishnan et al. are able to derive an effective atom-only action from which they uncover a wealth of new phenomena in this generalized configuration. One important result is that the phase transition to a crystal arrangement is first order and persists down to zero temperature. This represents a genuine quantum phase transition that involves Thermal gas vs BEC vs disorder localised analogous to Brazovskii s transition where a uniform spatial distribution abruptly transforms into a stripe pattern. This phase transition at zero temperature is solely driven by quantum fluctuations of the particle fields, which are dynamically amplified and develop into macroscopic spatial-density variations. (This resembles the way that large-scale structures are supposed to have appeared from quantum noise in the early Universe.) The spatial correlations and the form of the emerging structures are determined by the wavevectors supported by the optical-resonator geometry. With the help of extra confinement potentials for the particles that are introduced by light sheets, the dimensions of the emerging patterns can be externally controlled. Models with several interacting layered planes can be implemented. As an extra bonus, the set-up includes a built-in non-destructive monitoring system by virtue of analysis of the scattered light fields. In particular, at near-zero temperature news & views Cold atoms and photons confined together in high-quality optical resonators self-organize into complicated crystalline structures that have an optical-wavelength scale. Complex solid-state phenomena can be studied in real time on directly observable scales. Pump laser Bragg planes Figure 1 Simulated stationary distribution of 1, high-field-seeking atoms in an optical resonator transversely illuminated by laser light. The atoms self-order in a crystalline structure with Bragg planes (dashed diagonal lines as a guide to the eye) maximizing the coherent scattering into the resonator mode as predicted and observed in refs 1 and. of the nucleation of new atomic quantum phases 5. Thus, real-time non-destructive monitoring of the dynamics of a quantum phase transition can be foreseen. As cavity quantum electrodynamics (QED) set-ups with single particles coupled to super-mirror resonators pose severe experimental σ challenges, theoretical considerations invoking degenerate quantum σ + gases were long considered to be thought experiments only. However, using the recent exciting developments m =+1 in the optical manipulation m = of ultracold gases, m several = 1 teams have now implemented cavity- QED systems involving Bose Einstein condensates and super mirrors. Up to a million atoms at close to T = can be trapped in the field of a few photons (or even a single one),7. These experiments enter the strong-coupling regime where coherent quantum coupling dominates dissipation by more than three orders of magnitude. Here, the optical potentials and thus the light forces have genuine quantum properties so that the light and the particles become dynamically entangled. As a consequence, the dynamics can lead to superpositions of light-field states associated with different atomic quantum phases as an exotic form of a Schrödinger-cat state. The strong coherent coupling of atoms and photons can also be used as a controllable prototype interface of photonic- and atombased quantum computing. Whereas ultracold atoms interact directly only at close distances, the modification of the light field induced by a single particle influences the optical potential for virtually all other particles in the system 8. This longrange interaction can be tailored through the mirror geometry, and acts in a similar way to acoustic phonons in solid crystals. This adds an extra dimension to optical-lattice physics with ultracold quantum gases, which is already one of the most fruitful areas at the boundary of atomic and solid-state physics 9, including the physics of phonons, polarons or momentum-space pairing of particles. The tremendous recent progress has now surpassed the limits in readily Jonathan Keeling Multimode cavity QED CONDMAT17 1

41 Spin wave polaritons 1 Introduction: Tunable multimode Cavity QED Density wave polaritons Superradiance transition Supermode density wave polariton condensation 3 Spin wave polaritons Effects of loss Spin glass Meissner-like effect Jonathan Keeling Multimode cavity QED CONDMAT17 15

42 Internal states: Effect of particle losses Dicke Hamiltonian: H = ωa a + i ω σ + i σ i + gσ x i (a + a) Adding other loss terms t ρ = i[h, ρ] + κl[â] + i Γ L[σ i ] + Γ φ L[σ z i ] L[X] = XρX (X Xρ + ρx X)/ Γ, Γ φ break S conservation. Mean field: confusing result: Always: Normal state unstable for g > gc Γφ, Γ no SR solution [Dalla Torre et al., PRA (Rapid) 1, Kirton & JK, PRL 17] Jonathan Keeling Multimode cavity QED CONDMAT17 1

43 Internal states: Effect of particle losses Dicke Hamiltonian: H = ωa a + i ω σ + i σ i + gσ x i (a + a) Adding other loss terms t ρ = i[h, ρ] + κl[â] + i Γ L[σ i ] + Γ φ L[σ z i ] L[X] = XρX (X Xρ + ρx X)/ Γ, Γ φ break S conservation. Mean field: confusing result: Always: Normal state unstable for g > gc Γφ, Γ no SR solution [Dalla Torre et al., PRA (Rapid) 1, Kirton & JK, PRL 17] Jonathan Keeling Multimode cavity QED CONDMAT17 1

44 Internal states: Effect of particle losses Dicke Hamiltonian: H = ωa a + i ω σ + i σ i + gσ x i (a + a) Adding other loss terms t ρ = i[h, ρ] + κl[â] + i Γ L[σ i ] + Γ φ L[σ z i ] L[X] = XρX (X Xρ + ρx X)/ Γ, Γ φ break S conservation. Mean field: confusing result: Always: Normal state unstable for g > gc Γφ, Γ no SR solution [Dalla Torre et al., PRA (Rapid) 1, Kirton & JK, PRL 17] Jonathan Keeling Multimode cavity QED CONDMAT17 1

45 Internal states: Effect of particle losses Dicke Hamiltonian: H = ωa a + i ω σ + i σ i + gσ x i (a + a) Adding other loss terms t ρ = i[h, ρ] + κl[â] + i Γ L[σ i ] + Γ φ L[σ z i ] L[X] = XρX (X Xρ + ρx X)/ Γ, Γ φ break S conservation. Mean field: confusing result: Always: Normal state unstable for g > gc Γφ, Γ no SR solution [Dalla Torre et al., PRA (Rapid) 1, Kirton & JK, PRL 17] Jonathan Keeling Multimode cavity QED CONDMAT17 1

46 Effect of particle losses Wigner function W (â = ˆx + i ˆp) Γ φ only: MFT no SR Asymptotic scaling N = 3: no symmetry breaking [Kirton & JK, PRL 17] Jonathan Keeling Multimode cavity QED CONDMAT17 17

47 Effect of particle losses Wigner function W (â = ˆx + i ˆp) Γ φ only: MFT no SR Asymptotic scaling (a) (c) (b) (d) N = 3: no symmetry breaking [Kirton & JK, PRL 17] Jonathan Keeling Multimode cavity QED CONDMAT17 17

48 Effect of particle losses Wigner function W (â = ˆx + i ˆp) Γ φ only: MFT no SR Asymptotic scaling (a) (c) (b) (d) N = 3: no symmetry breaking [Kirton & JK, PRL 17] Jonathan Keeling Multimode cavity QED CONDMAT17 17

49 Effect of particle losses Wigner function W (â = ˆx + i ˆp) Γ φ only: MFT no SR Asymptotic scaling (a) (c) (b) (d) N = 3: no symmetry breaking [Kirton & JK, PRL 17] Jonathan Keeling Multimode cavity QED CONDMAT17 17

50 Effect of particle losses Wigner function W (â = ˆx + i ˆp) Γ φ only: MFT no SR Asymptotic scaling (a) (c) (b) (d) N = 3: no symmetry breaking [Kirton & JK, PRL 17] Jonathan Keeling Multimode cavity QED CONDMAT17 17

51 Effect of particle losses Wigner function W (â = ˆx + i ˆp) Γ φ only: MFT no SR Asymptotic scaling (a) (b)..5 (c) (d) N = 3: no symmetry breaking [Kirton & JK, PRL 17] Jonathan Keeling Multimode cavity QED CONDMAT17 17

52 Effect of particle losses Wigner function W (â = ˆx + i ˆp) Γ φ only: MFT no SR Asymptotic scaling (a) (b)..5 (c) (d) N = 3: no symmetry breaking [Kirton & JK, PRL 17] Jonathan Keeling Multimode cavity QED CONDMAT17 17

53 Disordered atoms Multimode cavity, Hyperfine states, H eff = µ µ a µa µ + n ω σz n + Ωg Random atom positions quenched disorder Ξ µ (r n )σn(a x µ + a µ) µ Effective XY/Ising spin glass H eff = { σ J nσ x m x Ising n,m n,m σ n + σm XY, J nm = µ Ω g Ξ µ (r n )Ξ µ (r m ) µ [Gopalakrishnan, Lev and Goldbart. PRL 11, Phil. Mag. 1] Jonathan Keeling Multimode cavity QED CONDMAT17 18

54 Disordered atoms Multimode cavity, Hyperfine states, H eff = µ µ a µa µ + n ω σz n + Ωg Random atom positions quenched disorder Ξ µ (r n )σn(a x µ + a µ) µ Effective XY/Ising spin glass H eff = { σ J nσ x m x Ising n,m n,m σ n + σm XY, J nm = µ Ω g Ξ µ (r n )Ξ µ (r m ) µ [Gopalakrishnan, Lev and Goldbart. PRL 11, Phil. Mag. 1] Jonathan Keeling Multimode cavity QED CONDMAT17 18

55 Disordered atoms Multimode cavity, Hyperfine states, H eff = µ µ a µa µ + n ω σz n + Ωg Random atom positions quenched disorder Ξ µ (r n )σn(a x µ + a µ) µ Effective XY/Ising spin glass H eff = { σ J nσ x m x Ising n,m n,m σ n + σm XY, J nm = µ Ω g Ξ µ (r n )Ξ µ (r m ) µ [Gopalakrishnan, Lev and Goldbart. PRL 11, Phil. Mag. 1] Jonathan Keeling Multimode cavity QED CONDMAT17 18

56 Meissner-like effect 1 Introduction: Tunable multimode Cavity QED Density wave polaritons Superradiance transition Supermode density wave polariton condensation 3 Spin wave polaritons Effects of loss Spin glass Meissner-like effect Jonathan Keeling Multimode cavity QED CONDMAT17 19

57 Cavity QED and synthetic gauge fields [Spielman, PRA 9] scheme, hyperfine states A, B H = ( ) ( E ψ A ψ A + ( Qˆx) ) ( ) Ω/ ψa B Ω/ E B + ( + Qˆx) ψ B Atoms +Q Q Feedback Why? Meissner effect, Anderson-Higgs mechanism, confinement-deconfinement transition. How? Multimode cavity QED A B Jonathan Keeling Multimode cavity QED CONDMAT17

58 Cavity QED and synthetic gauge fields [Spielman, PRA 9] scheme, hyperfine states A, B H = ( ) ( E ψ A ψ A + ( Qˆx) ) ( ) Ω/ ψa B Ω/ E B + ( + Qˆx) ψ B Atoms +Q Q Feedback Why? Meissner effect, Anderson-Higgs mechanism, confinement-deconfinement transition. How? Multimode cavity QED A B Ground state: E (k) (k (E B E A )Qˆx Ω ) m Jonathan Keeling Multimode cavity QED CONDMAT17

59 Cavity QED and synthetic gauge fields [Spielman, PRA 9] scheme, hyperfine states A, B H = ( ) ( E ψ A ψ A + ( Qˆx) ) ( ) Ω/ ψa B Ω/ E B + ( + Qˆx) ψ B Atoms +Q Q Feedback Why? Meissner effect, Anderson-Higgs mechanism, confinement-deconfinement transition. How? Multimode cavity QED A B Ground state: E (k) (k (E B E A )Qˆx Ω ) m Jonathan Keeling Multimode cavity QED CONDMAT17

60 Cavity QED and synthetic gauge fields [Spielman, PRA 9] scheme, hyperfine states A, B H = ( ) ( E ψ A ψ A + ( Qˆx) ) ( ) Ω/ ψa B Ω/ E B + ( + Qˆx) ψ B Atoms +Q Q Feedback Why? Meissner effect, Anderson-Higgs mechanism, confinement-deconfinement transition. How? Multimode cavity QED A B Ground state: E (k) (k (E B E A )Qˆx Ω ) m Jonathan Keeling Multimode cavity QED CONDMAT17

61 Meissner-like physics: idea Follow Spielman scheme ( EA + ( Qˆx) Ω/ ) Ω/ E B + ( + Qˆx) E A, E B ϕ from cavity Stark shift Ground state E (k) (k Qˆx ϕ ) Multimode cqed local matter-light coupling Variable profile synthetic gauge field? Reciprocity: matter affects field [Ballantine et al. PRL 17] Jonathan Keeling Multimode cavity QED CONDMAT17 1

62 Meissner-like physics: idea Follow Spielman scheme ( EA + ( Qˆx) Ω/ ) Ω/ E B + ( + Qˆx) E A, E B ϕ from cavity Stark shift Ground state E (k) (k Qˆx ϕ ) Multimode cqed local matter-light coupling Variable profile synthetic gauge field? Reciprocity: matter affects field [Ballantine et al. PRL 17] Jonathan Keeling Multimode cavity QED CONDMAT17 1

63 Meissner-like physics: idea Follow Spielman scheme ( EA + ( Qˆx) Ω/ ) Ω/ E B + ( + Qˆx) E A, E B ϕ from cavity Stark shift Ground state E (k) (k Qˆx ϕ ) Multimode cqed local matter-light coupling Variable profile synthetic gauge field? Reciprocity: matter affects field [Ballantine et al. PRL 17] Jonathan Keeling Multimode cavity QED CONDMAT17 1

64 Meissner-like physics: idea Follow Spielman scheme ( EA + ( Qˆx) Ω/ ) Ω/ E B + ( + Qˆx) E A, E B ϕ from cavity Stark shift Ground state E (k) (k Qˆx ϕ ) Multimode cqed local matter-light coupling Variable profile synthetic gauge field? Reciprocity: matter affects field [Ballantine et al. PRL 17] Jonathan Keeling Multimode cavity QED CONDMAT17 1

65 Meissner-like physics: idea Follow Spielman scheme ( EA + ( Qˆx) Ω/ ) Ω/ E B + ( + Qˆx) E A, E B ϕ from cavity Stark shift Ground state E (k) (k Qˆx ϕ ) Multimode cqed local matter-light coupling Variable profile synthetic gauge field? Reciprocity: matter affects field [Ballantine et al. PRL 17] Jonathan Keeling Multimode cavity QED CONDMAT17 1

66 Meissner-like physics: setup Atoms: ( ) ( ψa i t = [ ψ B m + E ϕ + i q m ) x Ω/ Ω/ E ϕ i q m +... x Light: i t ϕ = [ δ ( l + r l ] ( ψa ψ B ) ] iκ NE ( ψ A ψ B ) ϕ. Low energy: ψ A ψ B = Q ( ψ imω x ψ ψ x ψ ) E + Ω ψ ϕ [Ballantine et al. PRL 17] ). Jonathan Keeling Multimode cavity QED CONDMAT17

67 Meissner-like physics: setup Atoms: ( ) ( ψa i t = [ ψ B m + E ϕ + i q m ) x Ω/ Ω/ E ϕ i q m +... x Light: i t ϕ = [ δ ( l + r l ] ( ψa ψ B ) ] iκ NE ( ψ A ψ B ) ϕ. Low energy: ψ A ψ B = Q ( ψ imω x ψ ψ x ψ ) E + Ω ψ ϕ [Ballantine et al. PRL 17] ). Jonathan Keeling Multimode cavity QED CONDMAT17

68 Meissner-like physics: setup Atoms: i t ψa ψb E ϕ + i mq x = + Ω/ m Light: i t ϕ = δ l + r l Ω/ E ϕ i mq x +... iκ NE ( ψa ψb ) ϕ ψa. ψb. Low energy: ψa ψb = E Q ψ x ψ ψ x ψ + ψ ϕ imω Ω [Ballantine et al. PRL 17] Jonathan Keeling Multimode cavity QED CONDMAT17

69 Meissner-like physics: setup Atoms: i t ψa ψb E ϕ + i mq x = + Ω/ m Light: i t ϕ = δ l + r l Ω/ E ϕ i mq x +... ψa. ψb iκ NE ( ψa ψb ) ϕ + f (r). Low energy: ψa ψb = E Q ψ x ψ ψ x ψ + ψ ϕ imω Ω [Ballantine et al. PRL 17] Jonathan Keeling Multimode cavity QED CONDMAT17

70 Meissner-like physics: numerical simulations Atoms Cavity light Synthetic field Consider f (r) such that ϕ y. Without feedback (E = ) for field With feedback Field expelled Cloud shrinks [Ballantine et al. PRL 17] Jonathan Keeling Multimode cavity QED CONDMAT17 3

71 Meissner-like physics: numerical simulations Atoms Cavity light Synthetic field Consider f (r) such that ϕ y. Without feedback (E = ) for field With feedback Field expelled Cloud shrinks [Ballantine et al. PRL 17] Jonathan Keeling Multimode cavity QED CONDMAT17 3

72 Meissner-like physics: numerical simulations Atoms Cavity light Synthetic field Consider f (r) such that ϕ y. Without feedback (E = ) for field With feedback Field expelled Cloud shrinks [Ballantine et al. PRL 17] Jonathan Keeling Multimode cavity QED CONDMAT17 3

73 Meissner-like physics: numerical simulations Atoms Cavity light Synthetic field Consider f (r) such that ϕ y. Without feedback (E = ) for field With feedback Field expelled Cloud shrinks [Ballantine et al. PRL 17] Jonathan Keeling Multimode cavity QED CONDMAT17 3

74 Acknowledgments Experiment (Stanford): Benjamin Lev Theory: Ben Simons (Cambridge), Joe Bhaseen (KCL), James Mayoh (Southampton) Sarang Gopalakrishnan (CUNY) Surya Ganguli, Jordan Cotler (Stanford) Peter Kirton, Kyle Ballantine, Laura Staffini (St Andrews) Jonathan Keeling Multimode cavity QED CONDMAT17

75 WE-Heraeus-Seminar: Condensates of Light Physikzentrum Bad Honnef, Germany 1th 17th JANUARY 18

76 Summary Many possibilities of multimode cavity QED Cavity Ω Ω ω level system Cavity Ω ω level system Supermode polariton condensation [Kolla r et al. Nat. Comms. 17] a b 1 3 y 1 3 y x 1 x Open Dicke model, κ, Γφ, Γ [Kirton & JK, PRL 17] (a ) (b ) (c) (d ) (e) (f ) y / a y / a Jonathan Keeling φ / f [a ]. 1 5 x / a Bz / f y / a ψa + ψb [a - ] Meissner like effect [Ballantine et al. PRL 17] 1 x / a Multimode cavity QED CONDMAT17 5

77 Jonathan Keeling Multimode cavity QED CONDMAT17

78 Beyond Dicke: Chaotic dynamics Jonathan Keeling Multimode cavity QED CONDMAT17 7

79 Bosons beyond Dicke single mode So far Ψ(r) = χ + χ 1 cos(qx) cos(qz) S = χ σχ. Generally Ψ(r) = n χ ne iqn r. Jonathan Keeling Multimode cavity QED CONDMAT17 8

80 Bosons beyond Dicke single mode So far Ψ(r) = χ + χ 1 cos(qx) cos(qz) S = χ σχ. Generally Ψ(r) = n χ ne iqn r. ) i t χ n = ω r ( n δ n,n V n,n (α) χ n Jonathan Keeling Multimode cavity QED CONDMAT17 8

81 Bosons beyond Dicke single mode So far Ψ(r) = χ + χ 1 cos(qx) cos(qz) S = χ σχ. Generally Ψ(r) = n χ ne iqn r. ) i t χ n = ω r ( n δ n,n V n,n (α) χ n i t α = (ω E χ nm () n,n χ n iκ)α ηe χ nm (1) n,n n,n n,n χ n Jonathan Keeling Multimode cavity QED CONDMAT17 8

82 Bosons beyond Dicke single mode So far Ψ(r) = χ + χ 1 cos(qx) cos(qz) S = χ σχ. Generally Ψ(r) = n χ ne iqn r. ) i t χ n = ω r ( n δ n,n V n,n (α) χ n i t α = (ω E χ nm () n,n χ n iκ)α ηe χ nm (1) n,n n,n Truncate n < n M Hysteresis at intermediate ω Cavity intensity, φ Dicke n M = n M =3 n M =5 n M = Pump field, η ω =. n,n χ n Jonathan Keeling Multimode cavity QED CONDMAT17 8

83 Bosons beyond Dicke single mode So far Ψ(r) = χ + χ 1 cos(qx) cos(qz) S = χ σχ. Generally Ψ(r) = n χ ne iqn r. ) i t χ n = ω r ( n δ n,n V n,n (α) χ n i t α = (ω E χ nm () n,n χ n iκ)α ηe χ nm (1) n,n n,n Truncate n < n M Hysteresis at intermediate ω Cavity intensity, φ Dicke n M = n M =3 n M =5 n M = Pump field, η ω =. n,n χ n Jonathan Keeling Multimode cavity QED CONDMAT17 8

84 Bosons beyond Dicke chaos Near resonance: irregular dynamics (NB ωpump ωcavity = ω), ω=1.88, P=.533 ω=1.88, P=.17 ω=1.88, P=.7, ω=1.5, P=.5 ω=1.5, P=.533 ω=1.5, P=.17 ω=1.5, P=.7, ω=1.17, P=.5 ω=1.17, P=.17 ω=1.17, P=.7, ω=1.17, P=.533 ω=.85, P=.37 ω=.85, P=.5 ω=.85, P=.533 ω=.85, P=.17 ω=.85, P=.7 8, ω=.75, P=.83 ω=.75, P=.37 ω=.75, P=.5 ω=.75, P=.533 ω=.75, P=.17 ω=.75, P=.7-8 8, ω=.15, P=.83 ω=.15, P=.37 ω=.15, P=.5 ω=.15, P=.533 ω=.15, P=.17 ω=.15, P= Time, t (ms) Time, t (ms) Time, t (ms) Time, t (ms) Jonathan Keeling Time, t (ms) Time, t (ms) Multimode cavity QED CONDMAT17 9

85 Bosons beyond Dicke chaos Near resonance: irregular dynamics (NB ωpump ωcavity = ω) 8 ω=1.88, P=.17 ω=1.88, P=.7 8 ω=1.5, P=.533 ω=1.5, P=.17 ω=1.5, P=.7 ω=1.17, P=.5 ω=1.17, P=.533 ω=1.17, P=.17 ω=1.17, P=.7 8, ω=.85, P=.37 ω=.85, P=.5 ω=.85, P=.533 ω=.85, P=.17 ω=.85, P=.7 8 8, P=.533, ω=1.5 E -88 P=.17, ω=1.5 E P=.5, ω=1.17 E -88 P=.533, ω=1.17 E -88 P=.17, ω=1.17 E P=.5, ω=.85 E -88 P=.533, ω=.85 E -88 P=.17, ω=.85 E P=.37, ω=.75 E P=.5, ω=.75 E P=.533, ω=.75 E P=.17, ω=.75 E ω=.75, P=.83 ω=.75, P=.37 ω=.75, P=.5 ω=.75, P=.533 ω=.75, P=.17 ω=.75, P= P=.83, ω=.15 E P=.37, ω=.15 E P=.5, ω=.15 E P=.533, ω=.15 E P=.17, ω=.15 E ω=.15, P=.83 ω=.15, P=.37 ω=.15, P=.5 ω=.15, P=.533 ω=.15, P=.17 ω=.15, P= Time, t (ms) Time, t (ms) Time, t (ms) Time, t (ms) Jonathan Keeling Time, t (ms) P=.7, ω=1.5 E P=.7, ω=1.88 E , P=.83, ω=.75 E P=.37, ω=.85 E 8 -, P=.17, ω=1.88 E P=.5, ω=1.5 E, 8 ω=1.88, P=.533 ω=1.5, P=.5 P=.533, ω=1.88 E, 3 1 P=.7, ω=1.17 E P=.7, ω=.85 E P=.7, ω=.75 E P=.7, ω=.15 E Time, t (ms) Multimode cavity QED CONDMAT17 9