Condensed Matter Without Matter Quantum Simulation with Photons

Transcription

1 Condensed Matter Without Matter Quantum Simulation with Photons Andrew Houck Princeton University Work supported by Packard Foundation, NSF, DARPA, ARO, IARPA

2 Condensed Matter Without Matter Princeton (Experiment) Devin Underwood Darius Sadri James Raftery Neereja Sundaresan Yanbing Liu Gengyan Zhang Srikanth Srinivasan (-> IBM) Will Shanks (-> IBM) Anthony Hoffman (->Notre Dame) Northwestern (Theory) Andy Li Jens Koch Yale (Theory) Steve Girvin Alex Petrescu Karyn Le Hur Princeton (Theory) Mykola Bordyuh Hakan Türeci Work supported by Packard Foundation, NSF, DARPA, ARO, IARPA

3 Many body physics with photons Greentree et al., Nat. Phys. 2, 856 (2006) Hartmann et al., Nat. Phys. 2, 849 (2006) Angelakis et al., PRA 76, (2007) Koch and Le Hur, PRA 80, (2009) Competition between hopping/on-site interaction Non-equlibirium particle number not conserved Easy to achieve steady state

4 Equilibrium vs Non-Equilibrium Phase Transitions Thermal Quantum Dissipative Kessler et al, PRA 86, (2012) Dynamical Phase Transition: Non-analytic behavior in time for a time-evolving system

5 Outline Making photons interact Localization-delocalization in cavity dimers Building large cavity arrays Future Prospects

6 Cavity Quantum Electrodynamics 2g = vacuum Rabi freq. κ = cavity decay rate γ = transverse decay rate Strong Coupling = g > κ, γ Hˆ ω = ω σ σ σ r 2 z 2 ( ) ( + a a g a + a ) 1 a ˆ

7 Circuit Implementation of Cavity QED 2g = vacuum Rabi freq. κ = cavity decay rate γ = transverse decay rate out transmission line cavity 10 µm 10 GHz in Artificial atom Theory: Blais et al., Phys. Rev. A 69, (2004)

8 Strong Coupling: Vacuum Rabi Splitting 2g ~ 350 MHz Very Strong Coupling! A. Wallraff et al, Nature (London) 431, 162 (2004)

9 Strong non-linearities Bishop et al. (Schoelkopf lab), Nature Physics, 5, 105 (2009)

10 Jaynes-Cummings Dimer H = H J. C. Left + H J. C. Right J ( a a + a a ) L R R L S. Schmidt et al. Physical Review B 82, (R) (2010) Competition between localization (self-trapped) and delocalized (oscillating) Effective photon-photon interaction decreases at N increases, delocalizing system Dissipation drives system from delocalized to localized state

11 Dissipation Driven Crossover

12 Phase diagram Initial Photon Number (log scale) Time

13 Device

14 Measurement setup

15 Observation of Phase Diagram arxiv:

16 Localized Behavior: Collapse and Revival arxiv:

17 Localization varying initial imbalance arxiv:

18 Observation of Phase Diagram arxiv:

19 Dissipation driven crossover arxiv:

20 Dissipation driven crossover No interactions With interactions arxiv:

21 Dimer Conclusions Observation of two dynamical phases as initial photon number is varied Dissipation drives transition from delocalized to localized state (dissipation driven self-trapping) arxiv:

22 Many body physics with photons Greentree et al., Nat. Phys. 2, 856 (2006) Hartmann et al., Nat. Phys. 2, 849 (2006) Angelakis et al., PRA 76, (2007) Koch and Le Hur, PRA 80, (2009) Competition between hopping/on-site interaction Non-equlibirium particle number not conserved Easy to achieve steady state Non-equilibrium quantum phase transitions predicted

23 Large cavity arrays

24 Large cavity arrays

25 Kagome lattice transmission spectrum

26 Bands in the kagome lattice Kagome Lattice Transmission Kagome Band Diagram Koch, Phys. Rev. A 82, (2010)

27 Pump Probe Experiment Monitor 8.249GHz Threshold power for probe varies with pump frequency

28 Scanning defect for local readout Create single lattice site defect with scanned sapphire Measure change in transmission as defect position is changed

29 Experimental setup Microwave lines Input: heavy attenuation Output: isolators and HEMT 20 mk XYZ stack Cu and µ-metal shields Movement Retract in Z each step Stage heats to 50 mk 2 minute settle time Heat sink plates Sapphire Defect Cavity lattice

30 Defect calibration Transmission Extracted defect size

31 Larger Kagome lattices 49 resonators No qubits (but notches for qubits) Probe with 2 mm sapphire square Al bridges supported by BCB (spin-on glass) to connect ground planes

32 Probing the Kagome lattice Normal mode weights

33 Probing the Kagome lattice Probing the center resonator

34 Imaging the highest frequency mode

35 Probing the Kagome lattice Probing the center resonator

36 Imaging mode near Dirac point

37 Scanning circuit QED Tunable coupling Local probe of cqed lattice Qubit statistics Shanks, et al., Nat. Commun. 4, 1991 (2013).

38 Experimental setup Microwave lines Input: heavy attenuation Output: isolators and HEMT 20 mk XYZ stack Cu and µ-metal shields Movement Retract in Z each step Stage heats to 50 mk 2 minute settle time Heat sink plates Magnet coil Qubit+ resonator Shanks, et al., Nat. Commun. 4, 1991 (2013).

39 Device design: qubit Transmon qubit Designed for 7 µm working distance Charging energy Ec ~ 350 MHz SU-8 crash pads 1 mm 4 mm Maximum frequency f01,max_~ 12 GHz 60 µm 40 µm 500 µm Shanks, et al., Nat. Commun. 4, 1991 (2013).

40 Transmission as a function of position Shanks, et al., Nat. Commun. 4, 1991 (2013).

41 Towards FQHE with photons Idea: coupling resonators via Josephson rings photon transfer by virtual excitations of Josephson ring Circulators to break time reversal symmetry Effective photon Hamiltonian: Jens Koch, AH, Le Hur, Girvin, PRA 82, (2010)

42 Towards FQHE with photons Idea: coupling resonators via Josephson rings photon transfer by virtual excitations of Josephson ring Circulators to break time reversal symmetry Effective photon Hamiltonian:

43 Multi-mode ultra-strong coupling (MMUSC) g o g m Krimer et al., PRA 89, (2014)

44 Device 0.7m m 25 mm 0.04 mm 0.68m cavity

45 Transmission Spectrum Fundamental mode = 92.7 MHz Kappa ~ 1-6 MHz Qubit

46 Flux Tuning the Qubit, Magnet

47 Flux Tuning the Qubit, Magnet One flux quantum

48 Dispersive Readout

49 Full Fluorescence Spectrum

50 Conclusion Observation of two dynamical phases and dissipation driven crossover in Jaynes Cummings dimer (arxiv: ) Arrays with up to 200 cavities possible with minimal disorder in cavity frequencies (Phys. Rev. A 86, (2012)) Scanned qubit probe provides means of local photon number measurement (Nat. Commun. 4, 1991 (2013)) Scanned dielectric probe can image modes in large arrays Passive non-reciprocal coupling elements exist (PRA 82, (2010))

51 g vs y - more data

52 Finding resonance

53 Al/BCB bridges

54 Vibrations

55 Fitting transmission for g

56 Effect of qubit chip on resonator frequency

57 Josephson junction