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arXiv:1702.06004 · Physical Review Letters

Nonclassical Photon Number Distribution in a Superconducting Cavity under a Squeezed Drive

Shingo Kono, Y. MASUYAMA, T. Ishikawa, Yutaka Tabuchi, Rekishu Yamazaki, Koji Usami, Kazuki Koshino, Yasunobu Nakamura

Published Jul 13, 2017• 60 citations
arXivHTMLPDF

Abstract

A superconducting qubit in the strong dispersive regime of circuit quantum electrodynamics is a powerful probe for microwave photons in a cavity mode. In this regime, a qubit excitation spectrum is split into multiple peaks, with each peak corresponding to an individual photon number in the cavity (discrete ac Stark shift). Here, we measure the qubit spectrum in a cavity that is driven continuously with a squeezed vacuum generated by a Josephson parametric amplifier. By fitting the obtained spectrum with a model which takes into account the finite qubit excitation power, we determine the photon number distribution, which reveals an even-odd photon number oscillation and quantitatively fulfills Klyshko's criterion for nonclassicality.

DOI
10.1103/physrevlett.119.023602

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A superconducting qubit in the strong dispersive regime of circuit quantum electrodynamics is a powerful probe for microwave photons in a cavity mode. In this regime, a qubit excitation spectrum is split into multiple peaks, with each peak corresponding to an individual photon number in the cavity (discrete ac Stark shift). Here, we measure the qubit spectrum in a cavity that is driven continuously with a squeezed vacuum generated by a Josephson parametric amplifier. By fitting the obtained spectrum with a model which takes into account the finite qubit excitation power, we determine the photon number distribution, which reveals an even-odd photon number oscillation and quantitatively fulfills Klyshko's criterion for nonclassicality.
We investigate the cavity excitation spectrum and the photon number distribution in a cavity QED system driven by a broadband squeezed vacuum. In an empty cavity, we show that only states with even number of photons can be measured under resonant condition since the squeezed vacuum consists of states with even number of photons only. When a single atom is trapped in the cavity, the strong coupling between the atom and cavity results in energy splittings of the system, and there exist two peaks in the cavity excitation spectrum at two-photon transition frequencies. At the central frequency, however, all photon states can be detected because of the interaction between the atom and cavity. Therefore, it can be used to detect whether a single atom is trapped in the cavity. We also show that the squeezed vacuum can promote multiphoton excitations in the cavity. Using a coherent probe field, it is possible to explore higher Jaynes-Cummings doublet even if the probe field intensity is very weak.
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We measure photon occupancy in a thin-film superconducting lumped element resonator coupled to a transmon qubit at 20mK20\phantom{\rule{0.16em}{0ex}}\mathrm{mK}20mK and find a nonlinear dependence on the applied microwave power. The transmon-resonator system was operated in the strong dispersive regime, where the ac Stark shift $(2\ensuremath{\chi})$ due to a single microwave photon present in the resonator was larger than the linewidth $(\mathrm{\ensuremath{\Gamma}})$ of the qubit transition. When the resonator was coherently driven at 5.474 325 GHz, the transition spectrum of the transmon at 4.982 GHz revealed well-resolved peaks, each corresponding to an individual photon number-state of the resonator. From the relative peak heights we obtain the occupancy of the photon states and the average photon occupancy n‾\overline{n}n of the resonator. We observe a nonlinear variation of n‾\overline{n}n with the applied drive power Prf{P}_{\mathrm{rf}}Prf​ for n‾<5\overline{n}<5n<5 and compare our results to numerical simulations of the system-bath master equation in the steady state, as well as to a semiclassical model for the resonator that includes the Jaynes-Cummings interaction between the transmon and the resonator. We find good quantitative agreement using both models and analysis reveals that the nonlinear behavior is principally due to shifts in the resonant frequency caused by a qubit-induced Jaynes-Cummings nonlinearity.
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We study the dynamics of a general quartic interaction Hamiltonian under the influence of dissipation and non-classical driving. In this scenario, we show that an effective Hartree-type decoupling yields a good approximation to the dynamics of the system. We find that the stationary states are squeezed vacuum states of the non-interacting system which are enhanced by the Q-factor of the cavity. We show that this effective interaction could be realised with a cascaded superconducting cavity-qubit system in the strong dispersive regime in a setup similar to recent experiments. The qubit non-linearity, therefore, does not significantly influence the highly squeezed intracavity microwave field but, for a range of parameters, enables quantum state tomography of the cavity.