Spontaneous crystallization of light and ultracold atoms

Transcription

1 Spontaneous crystallization of light and ultracold atoms COST MP1403 NANOSCALE QUANTUM OPTICS Helmut Ritsch Theoretische Physik Universität Innsbruck QLIGHTCRETE, Kreta, June 2016

2 People Claudiu Genes Francesco Piazza PostDocs s : Tobias Griesser Wolfgang Niedenzu Collaborations (theory): Peter Domokos, Andras Vukics, Janos Asboth (Budapest) Giovanna Morigi (Saarbrücken), Aurelian Dantan (Aarhus) Igor Mekhov (Oxford), David Vitali (Camerino), Hashem Zoubi (Hannover), M. Holland, J. Schachenmayer (JILA, Boulder) Ph.D s Laurin Ostermann Raimar Sandner Sebastian Krämer Stefan Ostermann Dominik Winterauer Valentin Torggler Daniela Holzmann David Plankensteiner Master students: Philipp Aumann

3 Collective scattering, self-ordering and quantum simulation in optical resonators Ordering forces in confined 1D optical structures Atom light crystallization of an laser illuminated ultra-cold gas

4 Basic Physics Quantum optics: dynamics of quantized light modes Ultracold gases: quantum particles in optical potentials Quantum optics with quantum gases: full quantum dynamics of light and matter waves in dispersive (non-resonant) regime light induces a quantized optical potential + atoms generate a quantum refractive index H. R., P Domokos, F. Brennecke, T. Esslinger, Rev. Mod. Phys., 2013

5 Part I: collective scattering and self-ordering in resonators

6 U,g Dispersive Cavity QED for matter waves: a = ω laser ω atom g atom go coupling strength g atomic width k... cavity linewidth U(x) = optical potential / photon = cavity frequency shift / atom g(x) = photon loss / atom = radiation pressure / photon U = g 2 /D a g = G g 2 /D a 2 Dispersive limit D a >> g U >> g atom-field interaction via optical potential U dipole force dominates radiation pressure Strong coupling re-defined U >> k >> g single atom shifts cavity in or out of resonance single photon creates an optical trap for an atom Ultrastrong coupling U >> Dw mode >> k single mode picture breaks down nonlinear coupled multi mode model

7 Atomic quantum dynamics in cavities Ultracold gas near T= 0 in a quantum optical lattice potential Da 2 2 U ( x): g cos ( kx) 2 0 g D 2 a 0 n=2 > n=3 g g ( x): g cos ( kx) D g a 0 n=4 effective single atom Hamiltonian

8 Hubbard model for a quantized single mode Looks similar to standard Bose Hubbard model but parameters for lattice dynamics are field operators

9 recall: phases of cavity generated lattices in thermodynamic limit Cavity creates extra effective long range attraction or repulsion => parameter regions with two stable phases => phase superpositions of Mott insulator + superfluid? bosons in thermodynamic limit: M. Lewenstein, G. Morigi et. al. (PRL 2007,2008) generalization to fermions: Morigi PRA 2008

10 Crystallisation of particles through superradiant scattering transverse laser pump: direct excitation of atoms from side! phase of scattered light depends on position x,z z x x collective pump strength R Field in cavity generated only by atoms R = 0 for random atomic distribution R ~ Ng for regular lattice (Bragg)

11 laser Two scatterers placed along cavity axis Cavity field as cavity a function field intensityof atom position 4 x x 1 x x-atom x-atom Maximum photon number for 0 and l distance Minimum photon number for l/2 distance l ordering give maximal field for high field seekers ordering is energetically favourable

12 cavity field creates optical forces forces on 2 atoms in cavity 2 Hopfield neurons atoms drawn towards antinodes where scattering is maximized!

13 pump axis Numerical simulations of coupled atom field dynamics 2D - particle motion starting from random distribution cavity axis particles spontaneously form crystalline order Bragg scattering creates N^2 `superradiance

14 Selfconsistent atom-field distribution odd sites pump power even sites critical point Selforganisation as an open system phase transition

15 Atom-field dynamics for large ensembles: => Vlasov-Maxwell equations (see G. Robb, M. Hemmerling) Continuous density model for atoms single particle distribution function mean field optical potential Vlasov + Maxwell equations phase diagram including diffusion Niedenzu, EPL 2011 ordering threshold at thermal equilibrium frequency shift of cavity pump laser opt. potential cavity damping temperature

16 K Baumann et al. Nature 464, (2010) Selforganization of a BEC at T ~ 0 (mean field) Two-mode BEC approximation => Tavis-Cummings model BEC Nagy, Domokos, PRL (2010), NJP 2011 Fernandez-Vidal, Morigi PRA (2010) Zwerger, Piazza Dicke Superradiant Phase transition (predicted by Hepp+Lieb 1973) threshold from quantum fluctuations

17 multiparticle quantum description of selforganization in a lattice Selfordering beyond mean field pump creates optical lattice with atoms in lowest band cavity field from scattered lattice light Effective Hubbard type Hamiltonian: pump amplitude determined by atomic distribution operator

18 full quantum regime (BH): self ordering phase transition in optical lattice Theory DMFT-calculation Experiments: ETH ( + Hamburg ) W. Hofstetter (2010) R. Bakhtiari, M. Thorwart, HR (2014) G. Morigi, 2016 older work; M. Lewenstein, G. Morigi et.al. PRL 2007, 2008 intermediate phase with coherence + diagonal order => supersolid R. Landig et. al, Nature 533, 2016 A. Hemmerich et.al., PRL 2016

19 Selfordering in laser fields with several distinct frequencies Field amplitudes: single frequency (mode 5) three colors (mode 2+3+4) x2 x2 x1 x1 At some positions particles scatter all colors

20 Forces and fields for two particles Equilibrium positions = positions with high scattering intensity

21 Particle field dynamics with (quantum) noise: guided Brownian motion Quasi-random walk between high scattering areas Time averaged position distribution Particles tend to stay close to positions of optimum scattering and trapping: adaptive light collection system system learns in time memorizes previous conditions

22 Sum of order parameters: system optimizes scattering and learns from the past Adaptive + learning light collection system

23 Alternative: disspative annealing turn on mode illumination fast switch slow switch system converges mostly to optimal states for both modes

24 Selfordering with multicolor pump at T=0 : => competitive quantum phase transitions multimode Tavis Cummings model Nonlinear coupled oscillator model with tailorable coupling: pump amplitudes + detunings as control

25 Interacting trapped quantum particles within a multimode cavity Particle-field Hamiltonian coupling vectors Effective Hamiltonian after field elimination yes, we can engineer coupling matrices Aij by choice of modes + pumps!

26 Example: implementation of Hopfield model, associative memory single occupations per site Example: 10 sites energy spectrum searched pattern is lowest energy state

27 ( Hopfield model associative memory ) fast switch slow switch state converges to searched pattern Is this a general purpose quantum simulator?? JI. Cirac + P. Zoller, Nat. Phys, 8:264, C. Noh + DG Angelakis, arxiv: v1

28 Part II : collective scattering in confined geometry in 1D (no mirrors)

29 Light induced interaction via collective scattering into waveguide (+ forces along a 1D trap) tapered fiber A. Rauschenbeutel, E. Polzik S. NicChormaic tapered fiber + chip S. Rolston, L. Orosco waveguide nanostructure D. Chang, I. Cirac et. al., PRL13 J. Kimble + more Idea: transverse illumination induces scatterers to self arrange in ordered structure induced by collective scattering => scattering model description

30 microscopic dynamic model of scattering and forces near fiber : --> scattering matrix approach single particle close to fibre: z z r i z i particle chain: free propagation between scatteres A C B z D A B C D A B C D A B C D field amplitudes are linearly coupled: P M(z) Force (Maxwell stress tensor) 1. multiply matrices 2. enforce correct boundary conditions 3. calculate fields + forces 4. Dynamics of particles (Deutsch/Philipps 1995, Asboth 2005)

31 two particles = double slit forces dynamic evolution negligible absorption dynamic evolution with strong absorption * particles scatter collectively and order at ¾ l distance * particles form a resonator and confine light

32 many particles dynamics: collective scattering, forces and friction outer particles act as Bragg mirrors and trap inner particles => system forms a self organized optical resonator

33 Many particles: ultracold gas trapped along or within a fiber ( Vlasov approach) Coupled equations for field E(z) :Helmholtz and spatial distribution f(z): Vlasov -Boltzmann polarizability density effective pump power Instability of homogeneous order at e x > T. Griesser, PRL 2013 (see also: Chang et.al, PRL 2013)

34 selfconsistent atom-field solution for e x > Atomic distribution band gap right wave left running Field distribution Outer particles act like mirrors to confine light and trap inner particles! self odered cavity QED system!

35 Higher order solutions for stronger pump Particles generate a series of coupled cavities for light => engineering and optimization done by the system itself!

36 Part III : free space atom-light crystallization

37 An ultracold gas trapped in counterpropagating laser beams fields have different frequency and/or polarization to avoid spatial interference => translation invariant optical dipole trap Gross Pitaevskii for cold gas Maxwell / Helmholtz for fields dispersive off resonant interaction : gas constitutes dynamic refractive index: light creates dynamic optical potential:

38 density fluctuations and instability in an optical dipole trap weak dipole trap roton instability (Kuritzky) above critical laser power density fluctuations => light fluctuations => more density fluctuations ordering instability at critical wavevector

39 crystallization to ordered phase above threshold: particle density = Bragg reflector the two fields are shifted: => aperiodic solution field intensities = optical lattice

40 ordering in an additional longitudinal trap * atoms create confined light cavity * light creates lattice trap for atoms

41 long range interaction and phonons linearized perturbations: dynamics of peak densities

42 phonon spectra : infinite range interaction => phonon gap solid state toy model with phonons at zero temperature

43 Summary and Outlook Collective light scattering leads to crystallisation of mobile particles in resonators, near fibres and even in free space Multiple frequencies enhance selfordering and coupling => self optimizing light collection system with memory => Hopfield memory model and quantum simulation Selfordering appears also in fibres with a continuum of light modes with particles forming the resonators themselves Free space selfordering (optical binding) appears also for point particles in broadband fields and blackbody radiation

44 Thanks! visitors welcome!

45 effective 2-body interaction narrow band radiation black body radiation Ordering instability Collapse instability

46 Light induced self-ordering in a 2D planar trap with random or blackbody illumination single dipole field: x Interference of scattered fields and incident fields creates long range interaction => optical potential Gripped by light: optical binding, K Dholakia, P Zemánek, Rev. Mod. Phys. 201 Superdiffusion in optically controlled active media A. Dogariu, Nature Photonics 6, , (2012) Controlling dispersion forces between small particles with artificially created random light fields, F. Scheffold, JJ. Saenz (2015)

47 Random light fields: X-polarized plane wave Pump along z y x effective interaction Interaction potential strength from collective scattering Instability condition: σ = L/l 2D random distribution under transverse illumination exhibts density instability! (like optical binding but with point dipoles+ random field)

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