We consider the dynamics of a disordered ensemble of qubits interacting with a single-mode photon field, which is described by an exactly solvable inhomogeneous Dicke model. In particular, we concentrate on the crossover from few-qubit systems to the system of many qubits and analyze how the collective behavior of a coupled qubit-cavity system emerges despite the broadening. We show that quantum interference effects survive in the mesoscopic regime---the dynamics of an entangled Bell state encoded into the qubit subsystem remains highly sensitive to the symmetry of the total wave function. Moreover, relaxation of these states is slowed down due to the formation of collective dark states weakly coupled to light. Dark states also significantly influence the dynamics of the excitations of a photon subsystem by absorbing them into the qubit subsystem and releasing quasiperiodically in time. We argue that the predicted phenomena can be useful in quantum technologies based on superconducting qubits. For instance, they provide tools to deeply probe both collective and quantum properties of such artificial macroscopic systems.
We consider the dynamics of a disordered ensemble of qubits interacting with a single-mode photon field, which is described by an exactly solvable inhomogeneous Dicke model. In particular, we concentrate on the crossover from few-qubit systems to the system of many qubits and analyze how the collective behavior of a coupled qubit-cavity system emerges despite the broadening. We show that quantum interference effects survive in the mesoscopic regime---the dynamics of an entangled Bell state encoded into the qubit subsystem remains highly sensitive to the symmetry of the total wave function. Moreover, relaxation of these states is slowed down due to the formation of collective dark states weakly coupled to light. Dark states also significantly influence the dynamics of the excitations of a photon subsystem by absorbing them into the qubit subsystem and releasing quasiperiodically in time. We argue that the predicted phenomena can be useful in quantum technologies based on superconducting qubits. For instance, they provide tools to deeply probe both collective and quantum properties of such artificial macroscopic systems.
We study theoretically the collective quantum dynamics occurring in various interacting superconducting qubit arrays (SQAs) in the presence of a spread of individual qubit frequencies. The interaction is provided by mutual inductive coupling between adjacent qubits (short-range Ising interaction) or inductive coupling to a low-dissipative resonator (long-range exchange interaction). In the absence of interaction, the Fourier transform of the temporal correlation function of the total polarization (z projection of the total spin), i.e., the dynamic susceptibility $C(\ensuremath{\omega})$, demonstrates a set of sharp small magnitude resonances corresponding to the transitions of individual superconducting qubits. We show that even a weak interaction between qubits can overcome the disorder with a simultaneous formation of the collective excited states. This collective behavior manifests itself by a single large resonance in $C(\ensuremath{\omega})$. In the presence of a weak nonresonant microwave photon field in the low-dissipative resonator, the positions of dominant resonances depend on the number of photons, i.e., the collective ac Stark effect. Coupling of an SQA to the transmission line allows a straightforward experimental access of the collective states in microwave transmission experiments and, at the same time, to employ SQAs as sensitive single-photon detectors.
Coupling between quantum emitters and modes of light is foundational to studies of quantum systems. Coherent interactions between matter and light have greatly advanced the development of quantum technologies. When an ensemble of atoms interacts with light that is confined within a cavity---a resonator for photons---light also mediates atom-atom interactions, leading to collective phenomena that cannot be extrapolated from microscopic behaviors. Understanding how interactions among quantum particles lead to macroscopic phenomena, such as phase transitions and breaking of symmetries, remains a challenge in modern physics. In this dissertation, I present results addressing this challenge in the context of mesoscopic arrays of optical-tweezer-trapped atoms interfaced with a high-finesse optical cavity. In particular, the physics we investigate arises from the collective scattering of light. Utilizing the ability to place atoms with nanometer-scale precision, we engineer superradiant and subradiant states, where control over interference of the emission from multiple atoms leads to collectively enhanced or suppressed amounts of scattered light. Building on this work, we investigate the emergence of optomechanical self-organization, mediated by superradiance in the cavity electromagnetic field. By coupling atoms to the same cavity mode, the atoms exert forces on one another through the exchange of photons, leading them to autonomously order themselves spatially. We characterize mesoscopic fluctuations and their effect on symmetry-breaking dynamics associated with self-organization. Finally, we extend this framework to theoretically investigate how the phase of the atom-cavity coupling can be altered to generate higher symmetries. Our analysis reveals first-order phase transitions and instabilities induced by non-reciprocal forces. Altogether, this work establishes a path towards realizing mesoscopic systems of complex phases of matter in cavity quantum electrodynamics with unprecedented programmability.
We study quantum dynamics of many-qubit systems strongly coupled to a quantized electromagnetic cavity field in the presence of decoherence and dissipation for both quantum emitters and cavity photons, taking into account the varying coupling strength of different qubits to the cavity field and the spread of their transition frequencies. Compact analytic solutions for time-dependent quantum state amplitudes and observables are derived for a broad class of open quantum systems in Lindblad approximation with the use of the stochastic Schr\"odinger equation approach. We show that depending on the initial quantum state preparation, an ensemble of qubits can evolve into a rich variety of many-qubit entangled states with destructive or constructive interference between the qubits. In particular, when only a small fraction of qubits are initially excited, the dissipation in a cavity will inevitably drive the system into robust dark states that are completely decoupled from the cavity and live much longer than the decay time of the cavity field. We also determine the conditions under which coherent coupling to the quantized cavity field overcomes the dephasing caused by a spread of transition frequencies in multiqubit systems and leads to the formation of a decoupled dark state.
Collective light-matter phenomena such as Dicke superradiance are often described as a collection of effective spins coupled homogeneously to a bosonic mode, giving rise to a collective bright mode with enhanced light-matter coupling. In fermionic systems, Pauli exclusion and Fermi-surface structure can significantly modify this picture, while randomness in the atom-light couplings raises the question of whether disorder promotes or suppresses collective behavior. Here, we study a cavity model in which fermionic particles couple to a photonic mode through a random all-to-all interaction matrix with tunable mean and variance. Combining numerical mean-field methods, analytic stability analysis and random-matrix predictions, and benchmarks against exact diagonalization, we characterize both the onset and structure of the superradiant phase. While mean coupling and disorder variance contribute in the same way to the onset, they lead to drastically different behavior within the condensed phase. Uniform coupling supports a single bright collective fermionic mode with conventional Dicke-like scaling of the cavity field. Disorder, instead, gives rise to a qualitatively different collective regime in which many grey fermionic states participate coherently, producing a parametrically enhanced scaling of the condensate with system size. Our results reveal a mechanism through which disorder can, perhaps counterintuitively, promote collective light-matter phenomena.
We study quantum dynamics of many-qubit systems strongly coupled to a quantized electromagnetic cavity mode, in the presence of decoherence and dissipation for both fermions and cavity photons. The analytic solutions are derived for a broad class of open quantum systems in Lindblad approximation. They include identical qubits, an ensemble of qubits with a broad distribution of transition frequencies, and multi-level electron systems. Compact analytic solutions for time-dependent quantum state amplitudes and observables become possible with the use of the stochastic equation of evolution for the state vector. We show that depending on the initial quantum state preparation, the systems can evolve into a rich variety of entangled states with destructive or constructive interference between the qubits. In particular, dissipation in a cavity can drive the system into the dark states completely decoupled from the cavity modes. We also find the regimes in which multi-electron systems with a broad distribution of transition frequencies couple to the quantized cavity field as a giant collective dipole.
We propose a concept of mixed analog–digital quantum simulation of the Dicke model with ensembles of superconducting qubits coupled to the single-mode microwave resonators. Using both single-qubit and twoqubit quantum logic gates, it should be possible to engineer different initial conditions for the ensemble of qubits. Since qubits can interact through the photon field of a common quantum resonator, it is attractive to examine the time evolution of this system depending on various characteristics of the initial state, including entanglement and symmetry. We here study theoretically the dynamics of such systems taking into account energy dissipation, pure decoherence as well as disorder in qubits excitation frequencies, which are unavoidable for macroscopic artificial quantum systems. We reveal unusual effects of these imperfections on the dynamics.