Strongly Driven Semiconductor Double Quantum Dots. Jason Petta Physics Department, Princeton University

Transcription

1 Strongly Driven Semiconductor Double Quantum Dots Jason Petta Physics Department, Princeton University

2 Lecture 3: Cavity-Coupled Double Quantum Dots Circuit QED Charge-Cavity Coupling Towards Spin-Cavity Coupling Quantum Dot Maser

3 Cavity Quantum Electrodynamics Kimble Group, Caltech Circuit Quantum Electrodynamics (cqed) Blais (2004), Wallraff (2004), DiCarlo (2010)

4 Coupling Superconducting Qubits Via a Cavity Bus Majer et al. Nature (2007) Sillanpää et al. Nature (2007)

5 Spin Qubit Analog to cqed? superconducting resonator spin-orbit qubit + =? Schuster (2007) Nadj-Perge (2010) Trif, Golovach, Loss (2008)

6 Quantum Dot-Superconductor Hybrid System: Circuit 300 K 3 K 10 mk Resonator S 1 mm D 10 µm 100 nm dc biased cavity: Chen et al., APL (2011) GaAs: Frey et al., PRL (2012), Toida et al., PRL (2013), CNT: Delbecq et al., PRL (2011) K. D. Petersson, L. W. McFaul, J. M. Taylor, A. A. Houck, J. R. Petta, Nature (2012)

7 Bottom Gated InAs Nanowire Double Dots Nadj-Perge et al., Nature (2010) Schroer, Petersson, Jung, Petta, PRL (2011)

8 Charge Sensing Via the Cavity resonator phase response 1 mm K. D. Petersson, L. W. McFaul, J. M. Taylor, A. A. Houck, J. R. Petta, Nature (2012)

9 Interdot Charge Transitions S R L,C L R M,C M R R,C R D V L V R K. D. Petersson, L. W. McFaul, J. M. Taylor, A. A. Houck, J. R. Petta, Nature (2012)

10 Cavity Response at Interdot Charge Transitions 0 V L (mv) V R (mv) Charge qubit ε H ~ σ Z t ~ 0 = + C σ X 2 Ω = σ ε 2 2 H U Z, Ω = + ε 4t 2 C H Energy U, D 0 2t c Resonator dipole coupling H D = δε cos( ωrt ) ~ σ Z δε 2 ε t cos( ωrt) σ Z Ω Ω σ C = X ε H U, T Ω σ Z 2 Total Hamiltonian δε ε + cos( ωrt) σ Z 2 Ω 2tC + σ Ω = X

11 Jaynes-Cummings Hamiltonian Transform to rotating frame and quantize the field: H tot with = 0a a + σ Z + geff ( aσ + + a σ ) 2 Ω 2t 0 = ω0 ωr, = ωr, geff = g0 Ω See: Quantum Optics by Walls and Milburn, Springer 2008 C Cavity QED (CQED) Circuit QED (cqed) Kimble Group Blais (2004), Wallraff (2004)

12 Charge-Cavity Coupling Rate, g/2π ~ 30 MHz atom-cavity detuning = ω a - ω r K. D. Petersson, L. W. McFaul, J. M. Taylor, A. A. Houck, J. R. Petta, Nature (2012)

13 Transport: EDSR K. D. Petersson, L. W. McFaul, J. M. Taylor, A. A. Houck, J. R. Petta, Nature (2012)

14 Spin State Readout

15 Coherent Spin Control and Readout τ Rabi = 17 ns K. D. Petersson, L. W. McFaul, J. M. Taylor, A. A. Houck, J. R. Petta, Nature (2012)

16 Inelastic Charge Transport in a Cavity-Coupled Semiconductor Double Quantum Dot Quantum Dot Micromaser Key Elements Gain medium: double quantum dot Cavity: microwave resonator Energy supply: V SD (battery) Theory: Childress et al., PRA (2004) Hauss et al., PRL (2008); Andre et al., PRA (2009) Cottet et al., PRB (2011); Jin et al., PRB (2011) Bergenfeldt et al., PRB (2012) Main Results: Gain Q Frequency Frequency RDQD on I Single electron tunneling results in microwave amplification with gain G ~ Experiment: Liu et al., PRL (2014) Liu et al., Science (2015) Free-running photon emission statistics are consistent with an above threshold maser. Experiment: Liu et al., Science (2015) Theory: Gullans et al., PRL (2015) The free-running emission can be injection-locked to an input tone. Experiment: Liu et al., PRA (2015) Drive Frequency

17 DC Transport in Double Quantum Dots S R 1,C 1 R M,C M R 2,C 2 D I D V L V R (1,0) (1,1) Finite bias triangles V L (V) t c /h (0,1) (1,0) (0,0) Γ R Γ L (0,0) (0,1) t c /h (0,1) (1,0) (1,1) Γ L Γ R V R (V)

18 Microwave Amplification Repumping Mechanism: P.-Q. Jin et al., PRB (2011)

19 Photon Emission (High Current)

20 Narrowing of the Cavity Resonance Y.-Y. Liu, K. D. Petersson, J. Stehlik, J. M. Taylor, J. R. Petta, PRL (2014) Related work: Viennot et al., PRB (2014); Stockklauser et al., PRL (2015) Repumping Mechanism: P.-Q. Jin et al., PRB (2011)

21 Cooperativity Parameter CC = Good Coupling Bad Coupling = gg2 κκκκ gg = vacuum Rabi frequency ~ 30 MHz κκ = cavity decay rate ~ 3 MHz γγ = qubit decay rate ~ 500 MHz CC ~ 0.6 Anything will lase if you hit it hard enough Arthur Schawlow Nobel Prize in 1981 Photo: Wikipedia

22 Two Atoms in a Cavity: Double-Double 1 mm Left DQD Right DQD P in κ in S D ε L ε R κ out S D P out Quantum Dot Gain Medium Cavity gain G = P out /P in Yinyu Liu

23 Maser Action? G 10 1 Gain ~1000x LDQD Off On Off On RDQD Off Off On On 10 0 f c = MHz f in (MHz) 7884 Gain peak ~100 times narrower than the bare cavity resonance!

24 Free Running Maser Emission: Temporal Coherence 8 Data S(f) (pw/mhz) 4 34 khz Fit f (MHz) Peak full-width at half-maximum f = 34 khz Coherence time τ coh = 1/(π f ) = 9.4 µs Coherence length l coh = c τ coh = 2.8 km

25 Comparison with the Schawlow-Townes Limit Phasor diagram (in rotating frame) resulting field (I + I i ) 1/2 1 θ i random kick due to spontaneous emission Im(E) φ i I 1/2 (field due to stimulated emission) φ Re(E) Schawlow-Townes linewidth prediction Δ f = πππff cc κκ 2ππ PP tttttt Measured linewidth Δ f = 34 khz Schawlow and Townes, Phys. Rev. 112, 1940 (1958) Henry, IEEE Quant. Elec. 18, 259 (1982) 2 = 0.4 khz

26 Statistics of the Emitted Radiation Thermal Source Stable Oscillator Source: Siegman, Lasers Experimental Challenges Optical photon energy E = hν ~ 2 ev >> k B T (use off the shelf detectors) Microwave photon energy E = hν = 30 µev << k B T (no off the shelf detectors) Leading effort by the Wallraff Group: Bozyigit et al., Nature (2011)

27 Statistics of the Emitted Radiation Below Threshold Counts Q p n (%) 10 5 Data Poisson Thermal I n Above Threshold Counts 100 Q 0 RDQD on p n (%) Data Gaussian Thermal I n

28 Other Characteristics of the Double Dot Micromaser charge noise phonons (lattice vibrations) 100 I(t) [a.u.] t (μs)

29 Electric-Dipole + Electron-Phonon Interaction 7 gain G 1 S loss D S D Gain feature is very broad 100 µev ~ 25 GHz Liu et al., Science (2015) ε (mev) 1 2 Theory: Gullans et al., PRL (2015) Related work: Brandes, Phys. Rep. (2005); Kulkarni et al., PRB (2014)

30 Injection Locking Left DQD Right DQD f in, P in κ in S D ε L ε R κ out S D P out Adler equations: dddd dddd + 2ππ ff iiii ff ee ff iiii PP iiii PPee = ππδff iiii sin φφ PP ee = free running emission power ff ee = free running emission frequency PP iiii = input power ff iiii = input frequency φφ = φφ oooooo φφ iiii Adler, Proc. IRE 34, 351 (1946) Quantum Dot Gain Medium Liu et al., PRA (2015) Δf in (MHz) f (MHz) Δf in = 0.48 MHz P in = -105 dbm f in (MHz) input signal input signal f (MHz) S (W/MHz) Δf in = 0.85 MHz P in = -100 dbm f in (MHz) S (W/MHz) P in (dbm)

31 Summary Circuit QED Charge-Cavity Coupling Towards Spin-Cavity Coupling Quantum Dot Maser

32 Petta Group Undergrads: T. Hartke A. Wollack Postdoc: C. Eichler Grad Students: F. Borjans T. Hazard Y. Liu X. Mi S. Sangtawesin G. Stehlik D. Zajac S. Zhang Collaborators: G. Burkard, M. Gullans, J. Taylor We are hiring. Contact me if you are interested: