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

S. Kono, Y. Masuyama, T. Ishikawa, Y. Tabuchi, R. Yamazaki, K. Usami, K. Koshino, and Y. Nakamura

Phys. Rev. Lett. 119, 023602 – Published 13 July 2017

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.

Received 13 February 2017

DOI:https://doi.org/10.1103/PhysRevLett.119.023602

Physics Subject Headings (PhySH)

Quantum optics with artificial atoms Superconducting qubits

Atomic, Molecular & Optical

Authors & Affiliations

S. Kono¹, Y. Masuyama¹, T. Ishikawa¹, Y. Tabuchi¹, R. Yamazaki¹, K. Usami¹, K. Koshino², and Y. Nakamura^1,3

¹Research Center for Advanced Science and Technology (RCAST), The University of Tokyo, Meguro-ku, Tokyo 153-8904, Japan
²College of Liberal Arts and Sciences, Tokyo Medical and Dental University, Ichikawa, Chiba 272-0827, Japan
³Center for Emergent Matter Science (CEMS), RIKEN, Wako, Saitama 351-0198, Japan

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Issue

Vol. 119, Iss. 2 — 14 July 2017

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Figure 1
(a) Schematic of the experimental setup with squeezed vacuum injection. A squeezed vacuum generated by a flux-driven JPA, as a cavity drive field at $ω_{s}$ , is injected into the cavity from port 2. The cavity probe field at $ω_{p}$ and the qubit drive field at $ω_{d}$ are input from port 1, and the transmission of the cavity probe field is measured. The cavity is designed to have asymmetric external coupling rates of $κ_{2} \approx 100 \times κ_{1}$ . For the thermal- and coherent-state injections, the connection to the JPA is switched to a heavily attenuated microwave line connected to the respective sources at room temperature. (b) Energy levels of a dispersively coupled qubit-cavity system. $| g ⟩$ and $| e ⟩$ label the ground and the first exited states, respectively, of the transmon qubit, and $| n ⟩$ $(n = 0, 1, 2, \dots)$ indicates the photon number states of the cavity. The cavity drive field generates the steady-state photon number distribution in the cavity (red dots).
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Figure 2
(a) Cavity transmission as a function of the qubit drive frequency $ω_{d}$ and the cavity probe frequency $ω_{p}$ . The transmission is normalized by the maximum peak value. White dashed lines indicate $ω_{p} = ω_{c} \pm χ$ . (b) Cross sections of (a) at $ω_{p} = ω_{c} \pm χ$ (red and blue dots, respectively). Green lines represent the rigorous numerical results in which the finite cavity probe power is fully incorporated, whereas the black lines represent the numerical results within the linear response to the cavity probe field, which corresponds to the weak power limit of the cavity probe field. The splitting of the single-photon peak, which is observed for $ω_{p} = ω_{c} - χ$ (blue arrow), is understood as the Autler-Townes effect of the qubit, driven strongly at $ω_{d} = ω_{q} - 2 χ$ (see [31] for the details).
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Figure 3
(a)–(c) Qubit spectra reflecting the photon number distributions in the cavity. The cavity drive fields at frequency $ω_{s}$ are in (a) thermal, (b) coherent, and (c) squeezed vacuum states, respectively. The average photon number in each state is set to about 0.2. Blue dots are the experimental data, and the black solid lines are the numerically calculated linear responses. (d)–(f) Photon number distributions determined from the fittings (dots). Solid lines are the photon number distributions calculated from the corresponding models. (g) Klyshko’s figure of merit $K_{n}$ evaluated for each drive.
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Figure 4
(a)–(d) Squeezed-drive-frequency dependence of the qubit spectrum. $δ = ω_{s} - (ω_{c} + χ)$ is the detuning between the center frequency $ω_{s}$ of the squeezed vacuum field and the cavity resonant frequency $ω_{c} + χ$ . Blue dots are the experimental results, and black solid lines are the numerical calculations. (e)–(h) Photon number distributions determined from the fittings (dots and dashed lines). Solid lines in (e) and (h) are the photon number distributions calculated from the corresponding models. (i) Klyshko’s figure of merit $K_{n}$ evaluated for each detuning $δ$ .
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