Beyond Strong Coupling in a Multimode Cavity

Abstract

Here, we report an experimental realization of multimode strong coupling in cavity quantum electrodynamics. This novel regime is achieved when a single artificial atom is simultaneously strongly coupled to a large, but discrete, number of nondegenerate photonic modes of a cavity with coupling strengths comparable to the free spectral range. Our experiment reveals complex quantum multimode dynamics and spontaneous generation of quantum coherence, as evidenced by resonance fluorescence spanning many modes and ultranarrow linewidth emission. This work opens a new avenue for future experiments in light-matter interactions and poses a challenge to current theoretical approaches to its study. DOI: 10.1103/PhysRevX.5.021035 Subject Areas: Condensed Matter Physics, Photonics, Quantum PhysicsThe study of light-matter interaction has seen a resurgence in recent years, stimulated by highly controllable, precise, and modular experiments in cavity quantum electrodynamics (QED) [1]. The achievement of strong coupling [2][3][4], where the coupling between a single atom and fundamental cavity mode exceeds the decay rates, was a major milestone that opened the doors to a multitude of new investigations [5,6].Here, we investigate multimode strong coupling (MMSC) [7,8], where the coupling is comparable to the free spectral range (FSR) of the cavity; i.e., the rate at which a qubit can absorb a photon from the cavity is comparable to the roundtrip transit rate of a photon in the cavity. We realize, via the circuit QED architecture, an experiment accessing the MMSC regime and report remarkably widespread and highly structured resonance fluorescence. The observed drive dependence of the width, height, and position of the fluorescence peaks cannot be explained by cavity enhancement of sidebands observed in the single-mode regime [9]. As expounded below, our observations reveal a generation of coherence across multiple frequencies mediated by a single qubit and necessitate a multimode analysis. Beyond the novel phenomena presented here, the access to the MMSC regime opens up a new direction of exploration that is of interest both theoretically and experimentally.Interest in going beyond strong coupling has focused on the ultrastrong-coupling limit, where the breakdown of the rotating-wave approximation for the light-matter interaction results in excitation nonconserving terms [10][11][12][13]. In contrast, the direction which we pursue is the simultaneous strong coupling of the qubit to numerous modes, leading to qubit-mediated mode-mode interactions and nonlinear quantum dynamics not present in the single-mode problem. Thus, MMSC demonstrates a qualitatively new domain, intermediate between the quantum mechanics of systems with a small number of degrees of freedom and full continuum quantum field theory in free space. Unlike the traditional spin-boson problem that involves a bosonic continuum with an algebraic bath spectral function of the type JðωÞ ¼ αω s , the MMSC regime is described by a structured spectral function with an infi...

Quantum electrodynamics near a photonic bandgap

“…In contrast to electronic band-gap systems, even multiple photons can be simultaneously localized by a single atom, and the coherent photonic transport within the otherwise forbidden band-gap can have a strongly correlated nature [10, 2,12]. In contrast to a system with discrete cavity modes, which is well described by the single mode or multimode Jaynes-Cummings Hamiltonian [16,17,18], a continuous density of states enables the formation of a localized state in the band gap. While other spin-boson problems with continuous DOS have also been studied experimentally [19,20] or theoretically [21,22] with superconducting circuits, this work explores physics near the band edge, where localized states emerge and reservoir engineering becomes possible.…”

Convergence of the multimode quantum Rabi model of circuit quantum electrodynamics

“…We consider a Hamiltonian in which each uncoupled harmonic mode of the resonator, with resonance frequency ω m and annihilation operatorâ m , is coupled to the transition between the bare atomic states |i , |j with energiesh i ,h j through a coupling strengthhg m,i,j [24,25]. We derive such a Hamiltonian by constructing a lumped element equivalent circuit, or Foster decomposition, of the transmission line resonator as represented in Fig.…”

Multi-mode ultra-strong coupling in circuit quantum electrodynamics

“…Using a quantum circuit model, we found a Bloch-Siegert shift induced by counter-rotating terms of up to χ BS = 2π × 62 MHz. Combining this architecture with high-impedance microwave resonators 27,37 and a smaller free spectral range, 7 we expect to reach even further into the multi-mode ultra-strong coupling regime to probe exotic states of light and matter. 16 …”

“…With strong coupling, 3 where the coupling is larger than the dissipation rates γ and κ of the atom and mode respectively, experiments such as photon-number resolution 4 or Schrödinger-cat revivals 5 have beautifully displayed the quantum physics of a single-atom coupled to the electromagnetic field of a single mode. As the field matures, circuits of larger complexity are explored, [6][7][8] opening the prospect of controllably studying systems that are theoretically and numerically difficult to understand.…”