Observation of the Unconventional Photon Blockade in the Microwave Domain
Résumé
We have observed the unconventional photon blockade effect for microwave photons using two coupled superconducting resonators. As opposed to the conventional blockade, only weakly nonlinear resonators are required. The blockade is revealed through measurements of the second order correlation function g ð2Þ ðtÞ of the microwave field inside one of the two resonators. The lowest measured value of g ð2Þ ð0Þ is 0.4 for a resonator population of approximately 10 −2 photons. The time evolution of g ð2Þ ðtÞ exhibits an oscillatory behavior, which is characteristic of the unconventional photon blockade. Photon blockade is observed when a single two-level emitter, such as an atom [1], a quantum dot [2], or a superconducting qubit [3,4] is strongly coupled to a cavity, thus limiting the occupation of the cavity mode to zero or one photon. The second order correlation function g ð2Þ ðtÞ of the light leaking out of the cavity shows a dip at short time with g ð2Þ ð0Þ < 1, a signature of nonclassical fluctuations corresponding to antibunched photons. The same effect is predicted for a nonlinear Kerr cavity when the Kerr nonlinearity U is much larger than the cavity linewidth κ [5]. In 2010, Liew and Savona discovered that this constraint can be relaxed by considering two coupled cavities instead of one [6]. They found that perfect blockade g ð2Þ ð0Þ ¼ 0 can be achieved even for a vanishingly small ratio U=κ and named the effect "unconventional photon blockade" (UPB). The UPB was later interpreted as an interference between the two possible paths from the one to the two photon state [7] or as the fact that the cavity state is a displaced squeezed state [8]. Such states are known to exhibit antibunching for well-chosen displacement and squeezing parameters [9-12]. Reaching the strong coupling regime between a cavity and an emitter, or a large U=κ in a Kerr cavity remains highly challenging, especially in the optical domain. Therefore, the UPB has attracted considerable attention [13] by opening new possibilities to obtain sources of nonclassical light using readily available non-linear cavities forming a photonic molecule [14,15]. Here, we report on the observation of the UPB for microwave photons in a superconducting circuit consisting of two coupled resonators, one being linear and one weakly nonlinear [16]. We measure the moments of the two quadratures of the field inside the linear resonator using a linear amplifier [17,18]. The determination of g ð2Þ ð0Þ for an arbitrary field requires measuring the moments of the two quadratures up to the fourth order. But in the case of the UPB, the state of the field is expected to be a displaced squeezed Gaussian state; therefore the value of g ð2Þ ð0Þ can be accurately obtained from the measurement of the first and second order moments only. This greatly reduces the experimental acquisition time and allows us to perform an exhaustive study of the blockade phenomenon as a function of various experimental parameters. In particular, we have searched for the optimal g ð2Þ ð0Þ as a function of the resonator population. We also measure g ð2Þ ðtÞ and observe oscillations that are characteristic of the UPB. Finally, we confirm the validity of the Gaussian assumption through measurements of the moments up to the fourth order. Figure 1(a) shows a microscope image of the sample. Two resonators made of niobium and consisting of an inductance in series with a capacitance are coupled through a capacitance. The inductive part of the bottom resonator includes a SQUID that introduces a Kerr nonlinearity. Both resonators are coupled to two coplanar waveguides (CPW) that allow us to pump and probe the resonator fields. The effective Hamiltonian of the circuit is H=ℏ ¼ ω a a † a þ ω b b † b þ Jða † b þ b † aÞ − Ub † b † bb; ð1Þ where ω a is the resonance frequency of the top resonator, ω b is the resonance of the bottom resonator, which depends on the SQUID flux, J the coupling, and U the Kerr nonlinearity. As shown in Ref. [7], this Hamiltonian leads to a perfect blockade under the condition ω a ¼ ω b and U ¼ 2κ 3 =ð3 ffiffi ffi 3 p J 2 Þ, where κ is the loss rate of the reso-nators. The sample was designed to fulfill this condition with J ¼ 2π × 25, κ ¼ 2π × 8, and U ¼ 2π × 0.3 MHz. To check these values for our sample, we first measure the evolution of ω b with the SQUID flux as shown in Fig. 1(b). We assume that the bottom resonator can be modeled by a lumped element circuit formed by the association in series of a capacitor C, an inductance L, and the SQUID inductance L s , which varies with the applied flux ϕ as L s ¼ L s0 =j cosðπϕ=ϕ 0 Þj. From the red fit, we obtain L ¼ 1.09 nH and L s0 ¼ 81 pH. When ω b ≈ ω a ¼ 2π × 5.878 GHz, we obtain L s ¼ 337 pH, PHYSICAL REVIEW LETTERS 121, 043602 (2018) Editors' Suggestion Featured in Physics 0031-9007=18=121(4)=043602(5) 043602-1