Quantum simulation with superconducting circuits

Transcription

1 Quantum simulation with superconducting circuits Summary: introduction to quantum simulation with superconducting circuits: quantum metamaterials, qubits, resonators motional averaging/narrowing: theoretical overview simulation of motional averaging with a transmon - sample and experimental setup - random modulation square pulse modulation: beyond Landau-Zener three-level superconducting qubits (qutrits) conclusions Quantum Metamaterials Conference, June ,Spetses, Greece Sorin Paraoanu KVANTTI group Low Temperature Laboratory School of Science Aalto University, Finland

2 G. S. Paraoanu, Recent progress on quantum simulation using superconducting circuits, J. Low. Temp. Phys. 175, nos. 5/6 (014) Quantum simulators with superconducting circuits If life doles you quantum lemons, let s make quantum lemonade Seth Lloyd, as quoted in Nature 491, 3 (01)

3 Quantum computing DiVincenzo criteria 1.qubits.initialization 3.univ.set of quantum gates 4.readout 5.coherence Quantum simulation... just do it! S. Lloyd, Universal Quantum Simulators, Science 73, 1073 (1996) Digital: Trotter s formula!!! threshold theorem!!! Analog: Suppose that each ion also has a ~ Bloch-like ~ interaction with its environment characterized by parameters parameters T1, T, and ~.These parameters are determined by characteristics of the computer's environment [ ]. By tuning the ~ ~ computer's Bloch parameters so that T,,, the time over 1 T1 T T ~ which the computer interacts with its environment can be adjusted so that the decoherence and noise induced in the qubits of the computer by its environment simulate the decoherence and noise induced in the spins by their environment.

4 SQUID arrays: analogs of field theories in curved backgrounds Schwinger 1+1 QED, relativistic QFT in curved spacetimes, interacting fields, vacuum instabilities P. Lähteenmäki et. al., PNAS 110, 434 (013) Further: exploring the massless Klein-Gordon field with tunable speed x ( 1 x, t) c t ( x, t) 0 u Example: Hawking effect c c( x ut) T H k B c x P. D. Nation, M. P. Blencowe, A. J. Rimberg, and E. Buks, Phys. Rev. Lett. 103, (009) h

5 Open issues and further developments How and where DCE photons form (over several wavelengths, or locally) The role of decoherence Backaction (pump depletion) Qubits as Unruh-deWitt detectors Cosmological analogs Demonstrating the entanglement between regions in the vacuum state of a field Phase matching by resonators or qubits: travelingwave amplifiers

6 Emulation of spin systems Emulation of spin-1/, 1, and 3/ using a phase qubit M. Neeley, et. al., Science 35, 7 75 (009) Weak localization Yu Chen et. al. Nat. Commun. 5, 5184 (014) Many-body spin systems P. Macha et. al. Nat. Commun. 5, 5146 (014)

7 Bose-Hubbard models, Holstein polarons, SSH models, arrays of cavities V.M.Stojanovic et.al. Phys. Rev. B 89, (014) Motional averaging J.Li et. al., Nat. Commun. 4, 140 (013)

8 Motional averaging: theoretical aspects

9 ˆ ˆ ˆ ˆ ˆ ˆ ) ˆ( ) ˆ( ˆ ˆ ˆ ) ˆ( ˆ ) ˆ( ), ( ˆ ) ˆ( z z t t t t t H i dt t d! ) ( ) ( n t e t P n t n

10 without jumping with jumping width Numerical simulations: we use the quantum regression theorem and the method of quantum trajectories takes into account the shape of the pulses (finite rasing and lowering times) with sampling interval below 1 ns t ( t Poisson process with probability Pn ( t) e of n jumps in the time t n! ) n

11 Analytical results: for random processes for sine modulation ) / ( / 1 ) ( S ) ( 1 ) ( S 0 ) ( ) ( n J K S n n

12 Motional averaging with a transmon J. Li, M. P. Silveri, K. S. Kumar, J.-M. Pirkkalainen, A. Vepsäläinen, W. C. Chien, J. Tuorila, M. A. Sillanpää, P. J. Hakonen, E. V. Thuneberg, and G. S. Paraoanu, Motional averaging in a superconducting qubit Nature Comunications 4, 140 (013)

13 Sample: transmon [Yale, ETH,...] Schematic of the experiment Spectroscopy Transversal drive Modulation of the qubit frequency for the transmon:

14 Ω (MHz) Ω (MHz) Simulated and measured spectra with random modulation Ω Ω Ω Sections thought the spectrum for various modulation frequencies:

15 Rabi oscillations on hybrid qubit-modulation field states: Random modulation Sine modulation g k eff g J k

16

17 Motional averaging with a transmon qubit J.Li et. al., Nat. Commun. 4, 140 (013) Satisfies Lloyd s criteria Real system chemical potentials temperature, pressure Larmor frequency, T 1, T Simulator 0 1,,

18 Periodic modulation of the transition frequency of a transmon with strongly non-adiabatic pulses M. P. Silveri, K. S. Kumar, J. Li, J. Tuorila, A. Vepsäläinen, E. V. Thuneberg, and G. S. Paraoanu, Stückelberg interference in a superconducting qubit under periodic latching modulation New J. Phys. 17, (015)

19 Periodic latching... beyond the standard Landau-Zener formula novel transfer-matrix formalism developed... ( t) sgn[cost]... that allows us to calculate the time-averaged excited state occupation probability and identify the resonances/antiresonances f sq

20 Transfer-matrix formalism:

21 results: experiment vs. numerics and transfer-matrix theory frequency-detuning representation amplitude-detuning representation

22 S.Ashhab, J.R.Johansson, A.M.Zagoskin, and Franco Nori, PRA 75, (007)

23 Rotating wave approximation: f sq ( t) sgn[cost] f sin ( t) cost

24 difference between sine modulation (blue) and periodic latching modulation (black) along the second sideband [spectra shifted for clarity] red arrows are the antiresonances (coherent destruction of tunneling) for periodic latching modulation comparison between numerical results (black) and the rotating wave approximation (green) for the periodic latching modulation.

25 novel type of modulation: periodic latching modulation standard Landau-Zener formalism not applicable but the concept of Stückelberg phase and interference still valid experiment realized with a superconducting qubit (transmon) theoretical modeling: transfer matrix, rotating wave approximation, and numerical simulations theoretical predictions agree with experimental data

26 Three-level superconducting qubits

27 Autler-Townes effect

28 Review paper on 3-level systems J. Li, G. S. Paraoanu, K. Cicak, F. Altomare, J. I. Park, R. W. Simmonds, M. A. Sillanpää, and P. J. Hakonen, Decoherence, Autler-Townes effect, and dark states in two-tone driving of a three-level superconducting system, Phys. Rev. B 84, (011).

29 Measurements/data analysys done at LTL: Circuit parameter determination Rabi oscillation betwen higher excited levels (levels and 1)

30 Comparison between theory and experiment: (b) is a theoretical simulation of a model which includes cross-couplings and high-order levels (up to the 5th).

31 Dynamical control of absorbtion via the Autler-Townes effect Pulse sequence J. Li, G. S. Paraoanu, K. Cicak, F. Altomare, J. I. Park, R. W. Simmonds, M. A. Sillanpää, and P. J. Hakonen, Dynamical Autler-Townes control of a phase qubit, Sci. Rep., 645 (01).

32 On-resonant reflected power (a) with and (b) without cross-coupling Effects of (a) fixed relative phase between the probe and the coupling tones and (b) zero cross-coupling

33 Conclusions

34 SUMMARY Quantum simulation using Josephson metamaterials Two-level systems motional averaging for random frequency modulation the regime beyond LZ Three-level systems Autler-Townes effect time-domain control of the first transition by using the tone coupled to the second and third energy levels PROSPECTS the physics of the ultrastrong coupling regime (in a rotating frame). quantum metamaterials + transmons. fundamental aspects of quantum field theories.