Динамический эффект Лэмба в связанной системе сверхпроводникового кубита и СВЧ- резонатора Д. С. Шапиро, А. А. Жуков, В. В. Погосов, Ю. Е. Лозовик Центр. - презентация

1 Динамический эффект Лэмба в связанной системе сверхпроводникового кубита и СВЧ- резонатора Д. С. Шапиро, А. А. Жуков, В. В. Погосов, Ю. Е. Лозовик Центр фундаментальных и прикладных исследований, Всероссийский научно-исследовательский институт автоматики им. Н. Л. Духова (ГК «Росатом»), Москва НИТУ МИСиС, 2 июля 2015 г.

2 Motivation: cavity QED nonstationary effects Main idea: dynamical Lamb effect via tunable qubit-photon coupling Theoretical model: nonstationary Rabi model beyond RWA Results: system dynamics; a method to enhance the effect Summary Outline

3 Superconducting circuits with Josephson junctions First observation of the dynamical Casimir effect – tuning boundary condition for the electric field via an additional SQUID С. M. Wilson, G. Johansson, A. Pourkabirian, J. R. Johansson, T. Duty, F. Nori, P. Delsing, Nature (2011). Motivation-1 - Quantum computation (qubits) - A unique platform to study cavity QED nonstationary phenomena

4 Motivation-2 Casimir effect (1948) Two conducting planes attract each other due to vacuum fluctuations (zero-point energy)

5 Motivation-3 Dynamical Casimir effect: prediction (Moore, 1970) - Generation of photons (always in couples) - Difficult to observe in experiments with massive mirrors - Indirect schemes are needed

6 Motivation-4 Dynamical Casimir effect: first observation (2011) - Superconducting circuit system: high and fast tunability! - Statistics of photon states is in agreement with theory С. M. Wilson, G. Johansson, A. Pourkabirian, J. R. Johansson, T. Duty, F. Nori, P. Delsing, Nature (2011). tuning an inductance

7 Motivation-5 Natural atom in a nonstationary cavity А.А. Белов, Ю.Е. Лозовик, B.JI. Покровский, Лэмбовский сдвиг ридберговских атомов в резонаторе, ЖЭТФ (1989). N. B. Narozhny, A. M. Fedotov, and Yu. E. Lozovik, Dynamical Lamb effect versus dynamical Casimir effect, PRA (2001). Atom can be parametrically excited even if cavity sizes far exceed quantum-mechanical atom size

8 Motivation-6 Lamb shift: tiny shift of atom energy levels due to vacuum fluctuations. Dominant contribution to the shift is due to the zero-point fluctuations of photon field. Two channels of atom excitation (nonadiabatical modulation): - Absorption of Casimir photons - Nonadiabatical modulation of atomic level Lamb shift: dynamical Lamb effect. Excitation probability is proportional to the square of the Lamb shift modulation. Lamb shift for artificial macroscopic atoms (qubits) is not something illusive. Moreover, strong coupling regime is possible in contrast to natural atoms. A. Fragner, M. Goppl, J. M. Fink, M. Baur, R. Bianchetti, P. J. Leek, A. Blais, A. Wallraff, Science (2008).

9 Motivation-7 How dynamical Lamb effect can be isolated from other mechanisms of atom excitation? Fedotov, Narozhny, Lozovik, PRA (2001) Our idea is to suggest a realization of the dynamical Lamb effect in superconducting circuit systems (natural atom qubit). Difficult to implement !

10 Dynamically tunable qubit-resonator coupling - In contrast to the optical system with a natural atom, it is possible to dynamically tune also an effective photon-qubit coupling A. J. Hoffman, S. J. Srinivasan, J. M. Gambetta, A. A. Houck, Coherent control of a superconducting qubit with dynamically tunable qubit-cavity coupling, PRB (2011). M. S. Allman, F. Altomare, J. D. Whittaker, K. Cicak, D. Li, A. Sirois, J. Strong, J. D. Teufel, R.W. Simmonds, rf-SQUID-Mediated Coherent Tunable Coupling between a Superconducting Phase Qubit and a Lumped-Element Resonator, PRL (2010). S. Zeytino˘glu, M. Pechal, S. Berger, A. A. Abdumalikov Jr., A. Wallraff, S. FilippMicrowave-induced amplitude- and phase-tunable qubit-resonator coupling in circuit quantum electrodynamics, PRA (2015). … - This possibility makes superconducting qubit-resonator system a very promising candidate for the observation of the dynamical Lamb effect Main idea-1

11 Two possible realizations Dynamical coupling of a qubit (at rest !) with two resonators: nonadiabatic switching. Similar to the scheme with a natural atom A simplified scheme: dynamical coupling with a single resonator No Casimir photons! Main idea-2

12 Rabi model beyond the rotating wave approximation (one mode photon field) Stationary Lamb shift (perturbation theory in V): photons qubitcoupling Theoretical model-1

13 Qubit-photon coupling: RWA, conserves excitation number. Dressed states. Counter RWA term, a perturbation. Responsible for the Lamb shift V 1 -- slow Rabi oscillations of both the photon number and qubit state Theoretical model-2

14 Rotating wave approximation Theoretical model-3 Wave function Spectrum

15 Nonstationary system: qualitative picture after the coupling is turned on Fast and slow degrees of freedom: V 1 produces slow Rabi-like oscillations; V 2 generates fast oscillations (full resonance) Superposition of slow and fast oscillations Theoretical model-4 small parameter:

16 Hamiltonian splitting Slow oscillations appear automatically Theoretical model-5

17 + full resonance Probability of a parametric qubit excitation Results-1: single switching Excitation probability is proportional to the square of the Lamb shift modulation

18 An excellent agreement between a simple analytical treatment and numerics The effect, however, is very weak. Strong coupling regime? Number of generated photons Results-2: single switching

19 Huge enhancement of excitation probability ! Results-3: parametric driving -- integrands are not oscillating in sign

20 Photon states are strongly squeezed Results-4: parametric driving

21 Results-5: parametric driving First-order photon correlation function Second-order photon correlation function

22 Universal behavior Results-6: parametric driving - Qualitatively correct result, but quantitatively not so good. - Universality, however, does exist

23 Squeezing Results-7: parametric driving

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25 How to observe experimentally? Photon field: - Parametric excitation of photons - Statistics of photon states is different from statistics for Casimir photons (both even and odd states are populated) - Slow Rabi-like oscillations of various photon characteristics photons are coupled to a qubit. Results-9: possible experiment Dynamical Lamb effect can be parasitic for a quantum computation: uncontrollable qubit excitation

26 Dynamical Lamb effect can be realized in tunable superconducting qubit-resonator systems Theoretical description of systems evolution upon the modulation of qubit-resonator coupling constant Parametric pumping as an efficient method to enhance the effect Summary D. S. Shapiro, A. A. Zhukov, W. V. Pogosov, Yu. E. Lozovik, Phys. Rev. A 91, (2015)

27 Частота резонатора – 10 GHz g – MHz Decoherence – 1-30 MHz or smaller in new transmons Quality factor 10^4 Resonator size - centimeter

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29 Дипольное приближение