We propose the use of coherent control of a multi-qubit--cavity QED system in order to explore novel phase transition phenomena in a general class of multi-qubit--cavity systems. In addition to atomic systems, the associated super-radiant phase transitions should be observable in a variety of solid-state experimental systems, including the technologically important case of interacting quantum dots coupled to an optical cavity mode.
We predict the existence of novel first-order phase transitions in a general class of multi-qubit-cavity systems. Apart from atomic systems, the associated super-radiant phase transition should be observable in a variety of solid-state experimental systems, including the technologically important case of interacting quantum dots coupled to an optical cavity mode.
We consider a condensate of ultra cold bosonic atoms in a linear optical cavity illuminated by a two-pump configuration where each pump is making different angles with the direction of the cavity axis. We show such configuration allows a smooth transition from a one-dimensional quantum optical lattice configuration to a two-dimensional quantum optical lattice configuration induced by the cavity-atom interaction. Using a Holstein-Primakoff transformation, we find out the atomic density profile of such self-organised ground state in the super-radiant phase as a function of the angular orientatio…
We study the nonequilibrium quantum phase transition of an Ising chain in a dissipative cavity driven by an external transverse light field. When driving and dissipation are in balance, the system can reach a nonequilibrium steady state which undergoes a super-radiant phase transition as the driving strength increases. Interestingly, the super-radiant field changes the effective bias of the Ising chain in return and drives its own transition between the ferromagnetic and paramagnetic phase. We study the rich physics in this system with sophisticated behavior, and investigate important issues i…
The Dicke model of cavity quantum electrodynamics is approximately realized in condensed matter when the cyclotron transition of a two-dimensional electron gas is nearly resonant with a cavity photon mode. We point out that in the strong coupling limit the Dicke model of cavity cyclotron resonance must be supplemented by a term that is quadratic in the cavity photon field and suppresses the model's transition to a super-radiant state. We develop the theory of graphene cavity cyclotron resonance and show that the quadratic term, which is absent in graphene's low-energy Dirac model Hamiltonian, …
The dynamical Casimir effect (DCE) predicts the generation of photons from the vacuum due to the parametric amplification of the quantum fluctuation of an electromagnetic field\cite{casimir1,casimir2}. The verification of such effect is still elusive in optical systems due to the very demanding requirements of its experimental implementation. This typically requires very fast changes of the boundary conditions of the problem, such as the high-frequency driving of the positions of the mirrors of a cavity accommodating the field. Here, we show that an ensemble of two-level atoms collectively cou…
We realize a spin-1 Dicke model using magnetic sub-levels of the lowest F=1 hyperfine level of $^{87}$Rb atoms confined to a high finesse cavity. We study this system under conditions of imbalanced driving, which is predicted to have a rich phase diagram of nonequilibrium phases and phase transitions. We observe both super-radiant and oscillatory phases from the cavity output spectra as predicted by theory. Exploring the system over a wide range of parameters, we obtain the boundaries between the normal, super-radiant and the oscillatory phases, and compare with a theoretical model.
We investigate the thermodynamics of a combined Dicke- and Ising-model which exhibits a rich phenomenology arising from the second order and quantum phase transitions from the respective models. The partition function is calculated using mean field theory, and the free energy is analyzed in detail to determine the complete phase diagram for the system. The analysis reveals both first- and second-order Dicke phase transitions into a super-radiant state, and the cavity mean-field in this regime acts as an effective magnetic field, which restricts the Ising chain dynamics to parameter ranges away…
We use a versatile model to evaluate the multipartite entanglement and the nonclassical light generation in optical parametric oscillators, exploring the differences between doubly and triply resonant cavity configurations. We demonstrate the entanglement of the pump mode with converted fields in both situations, and the fundamental differences of oscillators using parametric down conversion and four wave mixing processes as the intracavity amplification technique. The strong correlations involving the sidebands of the pump and converted fields gives the signatures of a rich dynamic of multipa…
We compare two approaches to refine the "linear model" of cavity optomechanics, in order to describe radiation pressure effects that are beyond first order in the coupling constant. We compare corrections derived from (I) a widely used phenomenological Hamiltonian that conserves the photon number and (II) a two-mode truncation of C. K. Law's microscopic model, which we take as the "true" Hamiltonian of the system. While these approaches agree at first order, the latter model does not conserve the photon number, resulting in challenging computations from second order onwards. Our numerics sugge…
We investigate the cavity excitation spectrum and the photon number distribution in a cavity QED system driven by a broadband squeezed vacuum. In an empty cavity, we show that only states with even number of photons can be measured under resonant condition since the squeezed vacuum consists of states with even number of photons only. When a single atom is trapped in the cavity, the strong coupling between the atom and cavity results in energy splittings of the system, and there exist two peaks in the cavity excitation spectrum at two-photon transition frequencies. At the central frequency, how…
The coupling between defects in diamond and a superconducting microwave resonator is studied in the nonlinear regime. Both negatively charged nitrogen-vacancy and P1 defects are explored. The measured cavity mode response exhibits strong nonlinearity near a spin resonance. Data is compared with theoretical predictions and a good agreement is obtained in a wide range of externally controlled parameters. The nonlinear effect under study in the current paper is expected to play a role in any cavity-based magnetic resonance imaging technique and to impose a fundamental limit upon its sensitivity.
We investigate the generation of non-classical states of spins coupled to a common cavity by means of a collective driving of the spins. We propose a control strategy using specifically designed series of short coherent and squeezing pulses, which have the key advantage of being experimentally implementable with the state-of-the art techniques. The parameters of the control sequence are found by means of optimization algorithms. We consider the cases of two and four spins, the goal being either to reach a well-defined target state or a state maximizing a measure of non-classicality. We discuss…
A major trend within the field of cavity QED is to boost the interaction strength between the cavity field and the atomic internal degrees of freedom of the trapped atom by decreasing the mode volume of the cavity. In such systems, it is natural to achieve strong atom-cavity coupling, where the coherent interaction strength exceeds the cavity linewidth, while the linewidth exceeds the atomic trap frequency. While most work focuses on coupling of photons to the internal degrees of freedom, additional rich dynamics can occur by considering the atomic motional degree of freedom as well. In partic…
The dynamics of arbitrary-order quantum correlations in a cavity magnon-polariton system are investigated based on the quantum master equation in the coherent state representation. The phenomena of Rabi-like oscillation and level repulsion of the average cavity-photon number agree remarkably well with existing experimental observations. The competing nature of coherent and incoherent components in these two cases is further revealed by the second-order quantum coherence of the cavity photons and magnons, which can be systematically tuned by the driving microwave and thermal bath. Our results d…
We study the quantum phase transition (QPT) in a non-Hermitian Tavis-Cummings (TC) model of experimentally accessible parameters, which is engineered with two drive fields applied to an ensemble of two-level systems (TLSs) and a cavity, respectively. When the two drive fields satisfy a given parameter-matching condition, the coupled cavity-TLS ensemble system can be described by an effective standard TC Hamiltonian in the rotating frame. In this ideal Hermitian case, the engineered TC model can exhibit the super-radiant QPT with spin conservation at an experimentally accessible critical coupli…
We study dynamical phases of a driven Bose-Einstein condensate coupled to the light field of a high-Q optical cavity. For high field seeking atoms at red detuning the system is known to show a transition from a spatially homogeneous steady-state to a self-organized regular lattice exhibiting super-radiant scattering into the cavity. For blue atom pump detuning the particles are repelled from the maxima of the light-induced optical potential suppressing scattering. We show that this generates a new dynamical instability of the self-ordered phase, leading to the appearance of self-ordered stable…
The field of cavity optomechanics has achieved groundbreaking photonic control and detection of mechanical oscillators, based on their coupling to linear electromagnetic modes. Lately, however, there is an uprising interest in exploring cavity nonlinearities as a powerful new resource in radiation-pressure interacting systems. Here, we present a flux-mediated optomechanical device combining a nonlinear Josephson-based superconducting quantum interference cavity with a mechanical nanobeam. We demonstrate how the intrinsic Kerr nonlinearity of the microwave circuit can be used for a counter-intu…
Synthetic dimensions based on particles' internal degrees of freedom, such as frequency, spatial modes and arrival time, have attracted significant attention. They offer ideal large-scale lattices to simulate nontrivial topological phenomena. Exploring more synthetic dimensions is one of the paths toward higher dimensional physics. In this work, we design and experimentally control the coupling among synthetic dimensions consisting of the intrinsic photonic orbital angular momentum and spin angular momentum degrees of freedom in a degenerate optical resonant cavity, which generates a periodica…
Information about quantum phase transitions in conventional condensed matter systems, must be sought by probing the matter system itself. By contrast, we show that mixed matter-light systems offer a distinct advantage in that the photon field carries clear signatures of the associated quantum critical phenomena. Having derived an accurate, size-consistent Hamiltonian for the photonic field in the well-known Dicke model, we predict striking behavior of the optical squeezing and photon statistics near the phase transition. The corresponding dynamics resemble those of a degenerate parametric ampl…
We analyse the problem of a single mode field interacting with a pair of two level atoms. The atoms enter and exit the cavity at different times. Instead of using constant coupling, we use time dependent couplings which represent the spatial dependence of the mode. Although the system evolution is adiabatic for most of the time, a previously unstudied energy crossing plays a key role in the system dynamics when the atoms have a time delay. We show that conditional atom-cavity entanglement can be generated, while for large photon numbers the entangled system has a behaviour which can be mapped …
The dissipative Dicke model exhibits a fascinating out-of-equilibrium many-body phase transition as a function of a coupling between a driven photonic cavity and numerous two-level atoms. We study the effect of a time-dependent parametric modulation of this coupling, and discover a rich phase diagram as a function of the modulation strength. We find that in addition to the established normal and super-radiant phases, a new phase with pulsed superradiance which we term dynamical normal phase appears when the system is parametrically driven. Employing different methods, we characterize the diffe…
We propose entangling operations based on the energy curvature couplings of encoded spin qubits to a superconducting cavity, exploring the non-linear qubit response to a gate voltage variation. For a two-qubit ($n$-qubit) entangling gate we explore acquired geometric phases via a time-modulated longitudinal $σ_z$-coupling, offering gate times of 10s of ns even when the qubits and the cavity are far detuned. No dipole moment is necessary: the qubit transverse $σ_x$-coupling to the resonator is zero at the full sweet spot of the encoded spin qubit of interest (a triple quantum dot three-electron…
We explore the quantum correlation distribution in multipartite quantum states based on the square of quantum discord (SQD). For tripartite quantum systems, we derive the necessary and sufficient condition for the SQD to satisfy the monogamy relation. Particularly, we prove that the SQD is monogamous for three-qubit pure states, based on which a genuine tripartite quantum correlation measure is introduced. In addition, we also address the quantum correlation distributions in four-qubit pure states. As an example, we investigate multipartite quantum correlations in the dynamical evolution of mu…
We study symmetry breaking at the Dicke quantum phase transition by coupling a motional degree of freedom of a Bose-Einstein condensate to the field of an optical cavity. Using an optical heterodyne detection scheme we observe symmetry breaking in real-time and distinguish the two superradiant phases. We explore the process of symmetry breaking in the presence of a small symmetry-breaking field, and study its dependence on the rate at which the critical point is crossed. Coherent switching between the two ordered phases is demonstrated.
We consider an optomechanical system composed by a trapped ion dispersively coupled to a single mode of a pumped optical cavity. We focus in a parameter range for which the semiclassical description predicts two clearly distinct equilibrium configurations in the limits of small and large photon pumping, while a bistable regime is found for intermediate pumping. This semiclassical description, however, is not valid in close proximity of the system transitions or when the mean photon number is low. Here we provide a numerical analysis of the fully quantum state in the few-photon regime, explorin…
We present a study of the electromagnetic control of nonclassicality of the outgoing light field in a single atom cavity QED system. By exploring the energy eigenvalues and eigenstates, we show that the eigenstates are similar to the Jaynes-Cummings ladder of eigenstates and can be optically controlled by an external control field. Tuning the control field frequency to the one photon resonance, we show the superbunching behavior in the outgoing light field can be observed at the frequency of one photon resonance. We also show that there exists a magic control field intensity at which two photo…
We propose to control spin-mixing dynamics in a gas of spinor atoms, via the combination of two off-resonant Raman transition pathways, enabled by a common cavity mode and a bichromatic pump laser. The mixing rate, which is proportional to the synthesized spin-exchange interaction strength, and the effective atomic quadratic Zeeman shift (QZS), can both be tuned by changing the pump laser parameters. Quench and driving dynamics of the atomic collective spin are shown to be controllable on a faster time scale than in existing experiments based on inherent spin-exchange collision interactions. T…
In quantum field theory, bare particles are dressed by a cloud of virtual particles to form physical particles. The virtual particles affect properties such as the mass and charge of the physical particles, and it is only these modified properties that can be measured in experiments, not the properties of the bare particles. The influence of virtual particles is prominent in the ultrastrong-coupling regime of cavity quantum electrodynamics (QED), which has recently been realized in several condensed-matter systems. In some of these systems, the effective interaction between atom-like transitio…
Controlling light-matter based quantum systems in the strong coupling regime allows for exploring quantum simulation of many-body physics in nowadays architectures. For instance, the atom-field interaction in a cavity QED network provides control and scalability for quantum information processing. Here, we propose the control of single- and two-body Jaynes-Cummings systems in a non-equilibrium scenario, which allows us to establish conditions for the coherent and incoherent interchange of polariton branches. Our findings provide a systematic approach to manipulate polaritons interchange, that …
Optical cavity QED provides a platform with which to explore quantum many-body physics in driven-dissipative systems. Single-mode cavities provide strong, infinite-range photon-mediated interactions among intracavity atoms. However, these global all-to-all couplings are limiting from the perspective of exploring quantum many-body physics beyond the mean-field approximation. The present work demonstrates that local couplings can be created using multimode cavity QED. This is established through measurements of the threshold of a superradiant, self-organization phase transition versus atomic pos…
Cooling of mesoscopic mechanical resonators represents a primary concern in cavity optomechanics. Here in the strong optomechanical coupling regime, we propose to dynamically control the cavity dissipation, which is able to significantly accelerate the cooling process while strongly suppressing the heating noise. Furthermore, the dynamic control is capable of overcoming quantum backaction and reducing the cooling limit by several orders of magnitude. The dynamic dissipation control provides new insights for tailoring the optomechanical interaction and offers the prospect of exploring macroscop…
Multimode cavity quantum electrodynamics ---where a two-level system interacts simultaneously with many cavity modes---provides a versatile framework for quantum information processing and quantum optics. Due to the combination of long coherence times and large interaction strengths, one of the leading experimental platforms for cavity QED involves coupling a superconducting circuit to a 3D microwave cavity. In this work, we realize a 3D multimode circuit QED system with single photon lifetimes of $2$ ms and cooperativities of $0.5-1.5\times10^9$ across 9 modes of a novel seamless cavity. We d…
The quantum walk is a dynamical protocol which describes the motion of spinful particles on a lattice. Also, it has been demonstrated to be a powerful platform to explore topological quantum matter. Recently, the quantum walk in coherent state space has been proposed theoretically and realized experimentally. However, due to the inherent characteristics of coherent states, it is challenging to control the number of photons when we need the coherent space to be a nearly orthogonal space in practice. Here, we demonstrate that the nonorthogonality of coherent sates, on the one hand can be cancell…
Simulation of topological superconductors and their competing orders using photon-mediated interactions
JILA, NIST and Department of Physics, University of Colorado, Boulder（科罗拉多大学博尔德分校物理系、NIST和JILA）；Center for Theory of Quantum Matter, University of Colorado, Boulder（科罗拉多大学博尔德分校量子物质理论中心）；Pritzker School of Molecular Engineering, University of Chicago（芝加哥大学普里茨克分子工程学院）
