Abstract
Condensed matter physics has been driven forward by significant experimental and theoretical progress in the study and understanding of equilibrium phase transitions based on symmetry and topology. However, nonequilibrium phase transitions have remained a challenge, in part due to their complexity in theoretical descriptions and the additional experimental difficulties in systematically controlling systems out of equilibrium. Here, we study a one-dimensional chain of 72 microwave cavities, each coupled to a superconducting qubit, and coherently drive the system into a nonequilibrium steady state. We find experimental evidence for a dissipative phase transition in the system in which the steady state changes dramatically as the mean photon number is increased. Near the boundary between the two observed phases, the system demonstrates bistability, with characteristic switching times as long as 60 ms -- far longer than any of the intrinsic rates known for the system. This experiment demonstrates the power of circuit QED systems for studying nonequilibrium condensed matter physics and paves the way for future experiments exploring nonequilbrium physics with many-body quantum optics.
Highlights
Over the past decades, there has been remarkable progress in studying both real and synthetic quantum materials
Condensed matter physics has been driven forward by significant experimental and theoretical progress in the study and understanding of equilibrium phase transitions based on symmetry and topology
We study a one-dimensional chain of 72 microwave cavities, each coupled to a superconducting qubit, and coherently drive the system into a nonequilibrium steady state
Summary
FIG. 1. 72-site circuit QED lattice. (a) Coplanar waveguide resonators, each with a bare cavity frequency ωc=2π 1⁄4 7.6ð2Þ GHz, are capacitively coupled to form a linear chain on a 35 × 35 mm chip. To experimentally study the nonequilibrium behavior of the device, we monitor the transmission (S21) across the lattice while varying the drive frequency and scanning the drive power over more than 5 orders of magnitude [Fig. 2(a)]. As we vary the mean photon number in the system by increasing the strength of the drive, we observe that a sudden change in system behavior occurs: transmission peaks split and at around −95 dBm of drive power, abruptly give way to a region of strongly suppressed transmission. Hhj;ojp0 , and a coherent drive (acting only on site 1) Hd. Each resonator contributes a single harmonic mode, Hrj 1⁄4 ħωca†j aj, where a†j and aj are the creation and annihilation operators for photons on site j and ωc is the fundamental frequency of the resonator. Within the quasiclassical treatment [24], the quadrature amplitudes αj 1⁄4 haji and βj 1⁄4 hbji play the role of mean-field parameters and obey the system of 144 nonlinear coupled equations: iα_ j 1⁄4
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