Cavity Decay Rate Research Articles

Generating multipartite entangled states of qubits distributed in different cavities

Cavity-based large-scale quantum information processing (QIP) needs a large number of qubits and placing all of them in a single cavity quickly runs into many fundamental and practical problems such as the increase of cavity decay rate and decrease of qubit-cavity coupling strength. Therefore, future QIP most likely will require quantum networks consisting of a large number of cavities, each hosting and coupled to multiple qubits. In this work, we propose a way to prepare a $W$-class entangled state of spatially-separated multiple qubits in different cavities, which are connected to a coupler qubit. Because no cavity photon is excited, decoherence caused by the cavity decay is greatly suppressed during the entanglement preparation. This proposal needs only one coupler qubit and one operational step, and does not require using a classical pulse, so that the engineering complexity is much reduced and the operation is greatly simplified. As an example of the experimental implementation, we further give a numerical analysis, which shows that high-fidelity generation of the $W$ state using three superconducting phase qubits each embedded in a one-dimensional transmission line resonator is feasible within the present circuit QED technique. The proposal is quite general and can be applied to accomplish the same task with other types of qubits such as superconducting flux qubits, charge qubits, quantum dots, nitrogen-vacancy centers and atoms.

Lasing and high-temperature phase transitions in atomic systems with dressed-state polaritons

We consider the fundamental problem of high temperature phase transitions in the system of high density two-level atoms off-resonantly interacting with a pump field in the presence of optical collisions (OCs) and placed in the cavity. OCs are considered in the framework of thermalization of atomic dressed state (DS) population. For the case of a strong atom-field coupling condition we analyze the problem of thermodynamically equilibrium superradiant phase transition for the order parameter representing a real amplitude of cavity mode and taking place as a result of atomic DSs thermalization process. Such transition is also connected with condensed (coherent) properties of low branch (LB) DS-polaritons occurring in the cavity. For describing non-equilibrium phase transitions we derive Maxwell-Bloch like equations which account for cavity decay rate, collisional decay rate and spontaneous emission. Various aspects of transitions to laser field formation by using atomic DS levels for both positive and negative detuning of a pump field from atomic transition frequency are studied in detail. It is revealed, that for positive atom-light detuning DS lasing can be obtained in the presence of quasi-equilibrium DS population that corresponds to a true two-level atomic system with the inversion in nonresonant limit.

Nonclassical mechanical states in an optomechanical micromaser analog

Here we show that quantum states of a mechanical oscillator can be generated in an optomechanical analog of the micromaser in the absence of any atomlike subsystem, thus exhibiting single-atom masing effects in a system composed solely of oscillator components. In the regime where the single-photon coupling strength is on the order of the cavity decay rate, a cavity mode with at most a single-excitation present gives rise to sub-Poissonian oscillator limit-cycles that generate quantum features in the steady state just above the renormalized cavity resonance frequency and mechanical sidebands. The merger of multiple stable limit-cycles markedly reduces these nonclassical signatures. Varying the cavity-resonator coupling strength, corresponding to the micromaser pump parameter, reveals transitions for the oscillator phonon number that are the hallmark of a micromaser. The connection to the micromaser allows for a physical understanding of how nonclassical states arise in this system and how best to maximize these signatures for experimental observation.

Cooling molecules in a two mode ring cavity

We derive dynamical equations for the motion of a molecule in a two mode ring cavity from a completely classical picture, including the molecular spontaneous decay and the cavity decay rates. The numerical results show that the molecule is trapped inside a single potential well and cooled on a timescale of order 10κ −1. The cooling process is strongly enhanced by modulating some parameters.

Control of sudden transition between classical and quantum correlations of two strongly driven atoms in dissipative cavities

We investigate analytically the dynamics of classical and quantum correlations between two strongly driven atoms, each of which is trapped inside a dissipative cavity. It is found that there exists a finite time interval during which the quantum discord initially prepared in the X-type states is not destroyed by the decay of the cavities. The sudden transition between classical correlation and quantum discord is sensitive to the initial-state parameter, the cavity decay rate, and the cavity mode-driving field detuning. Interestingly, we show that the transition time can be prolonged significantly by increasing the degree of the detuning.

Phase-dependent squeezing and entanglement in a cavity QED

The output squeezed spectrum of the output two modes from a cavity QED system which is embedded by a four-level atom driven by two classical fields are calculated. The effects of the cavity decay rates, relative phase between two classical fields, and effective coupling constants between the atom and the cavity on the entanglement and squeezing of the two cavity modes are investigated. It is shown that the depth of the squeezing or entanglement spectrum is insensitive to the cavity decay rates while its width is dependent on the cavity decay rates and the coupling constants. In particular, the squeezing or entanglement spectrum including their maximal values and widths is remarkably affected by the relative phase between the classical fields. It is found that the output spectrum varies with the relative phase in a cosine-like behavior with a period of 2π. The results can indicate how to suitably adjust the relative phase for acquiring maximal squeezing or perfect entanglement for the two cavity fields. This will be useful in quantum communication and computation.

Dissipative dynamics of quantum correlations in the strong-coupling regime

The dynamics of entanglement and quantum discord between two identical qubits strongly interacting with a common single mode leaky cavity field have been investigated beyond the rotating wave approximation (RWA) by using recently derived Lindblad type quantum optical master equation [F. Beaudoin, J.M. Gambetta, A. Blais, Phys. Rev. A {\bf 84}, 043832 (2011)] that can describe the losses of the cavity field in a strong atom-field coupling regime. Contrary to previous investigations of the same model in the dissipative regime by using the standard Lindblad quantum optical master equation in a strong-coupling regime, the atom-field steady states are found to be cavity decay rate independent and have a very simple structure determined solely by the overlap of initial atomic state with the subradiant state which is valid for all coupling regimes. Non-RWA dynamics are found to have remarkable effects on the steady state quantum discord and entanglement that cannot be achieved under RWA conditions, for instance, they can induce steady state entanglement even for the initial states that have no overlap with the subradiant state. Moreover, the non-RWA dynamics are found to reverse the initial state dependence of steady state entanglement and quantum discord contrary to the RWA case.

Single-photon nonlinearities in two-mode optomechanics

We present a detailed theoretical analysis of a weakly driven, multimode optomechanical system, in which two optical modes are strongly and near-resonantly coupled to a single mechanical mode via a three-wave mixing interaction. We calculate one- and two-time intensity correlations of the two optical fields and compare them to analogous correlations in atom-cavity systems. Nonclassical photon correlations arise when the optomechanical coupling $g$ exceeds the cavity decay rate $\ensuremath{\kappa}$, and we discuss signatures of one- and two-photon resonances as well as quantum interference. We also find a long-lived correlation that decays slowly with the mechanical decay rate $\ensuremath{\gamma}$, reflecting the heralded preparation of a single-phonon state after detection of a photon. Our results provide insight into the quantum regime of multimode optomechanics, with potential applications for quantum information processing with photons and phonons.

A quasi-continuous superradiant Raman laser with < 1 intracavity photon

Steady-state collective emission from ensembles of laser cooled atoms has been proposed as a method for generating sub-millihertz linewidth optical lasers, with potential for broad impacts across science and technology. We have built a model system that tests key predictions for such active oscillators using a Raman laser with laser cooled atoms as the gain medium. The laser operates deep in the bad-cavity, or superradiant, regime of laser physics, where the cavity decay rate is much greater than the atomic coherence decay rate. Specifically, we demonstrate that a system of 106 87Rb atoms trapped in a 1D standing wave optical lattice can spontaneously synchronize and collectively emit a quasi-continuous coherent optical output, even when the intracavity field contains on average < 1 photon.

Precision measurement of resonate frequency and the effective cavity length of the high finesse optical micro-cavity

Ultra-high finesse micro-resonator plays an important role in realizing the interaction between atoms and cavity field in the study of cavity quantum electrodynamics (QED) system, weak optical nonlinear effects and micro-optic devices. By measuring basic parameters of the microcavity, the atom-cavity coupling coefficient and the cavity decay rate can be determined precisely. It is also useful for exploring the dynamic characteristics of the system. However, it has difficulty in determining resonate frequency and effective cavity length due to the structure of the ultra-high finesse optical microcavity itself and the characteristics of multilayer coating. In this paper, we demonstrate the precision measurement of effective cavity length under different resonant frequencies which our cavity mirror is coated with 37 layers of dielectric film. The theoretical expectation when using the revised model of the multilayer coating agrees well with that of the experiment; and the measurement error for longitudinal mode interval is below 0.004 nm which is two orders of magnitude better than that obtained in previous unrevised model. The tiny depths into mirror coatings that the standing-wave light field inside the cavity penetrates are given for different mode numbers. This method may be applied to other micro resonator in the precision measurement.

Photon emission from a quantum dot-photonic crystal microcavity system: The role of pumping and cavity decay rates

We present a study of photon emission from a photonic crystal microcavity-quantum dot system. We take into account dissipative and pumping mechanisms consisting of the decay rate of cavity photons with the pumping rates of exciton and cavity. Numerically, we calculate the exciton state in a model quantum dot through the variational approach and photonic crystal microcavity L1 and modified-L1 modes through the GME (guided mode expansion) code, respectively. Second order correlation function of cavity (g(2)(τ)) and populations of photons and exciton have been obtained by using master equation and quantum regression theorem. Detailed investigation of the effect of pumping rates and cavity decay rate on the populations and g(2)(0) has been done in the steady state regime. Results demonstrate that when modified-L1 microcavity and exciton modes are off-resonance, detuning has opposite surprising effects on antibunching effect at different values of pumping rates.

Effect of the Casimir force on the entanglement between a levitated nanosphere and cavity modes

We investigate the effect of the Casimir force on the entanglement in an optomechanical system formed by a Fabry-P\'erot cavity with a dielectric nanosphere trapped near the cavity mirror by external driving laser beams. We find that steady-state optomechanical entanglement can be generated via the Casimir interaction between the nanosphere and the mirror, even with only one driving laser. With two driving lasers that are simultaneously responsible for trapping and cooling, the Casimir effect may enhance or reduce the degree of the steady-state optomechanical entanglement, depending on the cavity detunings, the strength of the Casimir interaction, the driving powers, and the cavity decay rates. The Casimir effect leads to an oscillation frequency shift of the nanosphere in the optomechanical system, which could be used for estimating the magnitude of the Casimir force between a sphere and a plane.

Non-Markovianity and Clauser-Horne-Shimony-Holt (CHSH)-Bell inequality violation in quantum dissipative systems

We examine the non-Markovian dynamics in a multipartite system of two initially correlated atomic qubits, each located in a single-mode leaky cavity and interacting with its own bosonic reservoir. We show the dominance of non-Markovian features, as quantified by the difference in fidelity of the evolved system with its density matrix at an earlier time, in three specific two-qubit partitions associated with the cavity-cavity and atom-reservoir density matrices within the same subsystem, and the cavity-reservoir reduced matrix across the two subsystems. The non-Markovianity in the cavity-cavity subsystem is seen to be optimized in the vicinity of the exceptional point. The Clauser-Horne-Shimony-Holt (CHSH)-Bell inequality computed for various two-qubit partitions show that high non-locality present in a specific subsystem appears in conjunction with enhanced non-Markovian dynamics in adjacent subsystems. This is in contrast to the matching existence of non-locality and quantum correlations in regions spanned by time t and the cavity decay rate, λ(c) for select partitions. We discuss the applicability of these results to photosynthetic systems.

Photon shot noise dephasing in the strong-dispersive limit of circuit QED

We study the photon shot noise dephasing of a superconducting transmon qubit in the strong-dispersive limit, due to the coupling of the qubit to its readout cavity. As each random arrival or departure of a photon is expected to completely dephase the qubit, we can control the rate at which the qubit experiences dephasing events by varying in situ the cavity mode population and decay rate. This allows us to verify a pure dephasing mechanism that matches theoretical predictions, and in fact explains the increased dephasing seen in recent transmon experiments as a function of cryostat temperature. We observe large increases in coherence times as the cavity is decoupled from the environment, and after implementing filtering find that the intrinsic coherence of small Josephson junctions when corrected with a single Hahn echo is greater than several hundred microseconds. Similar filtering and thermalization may be important for other qubit designs in order to prevent photon shot noise from becoming the dominant source of dephasing.

Controllable-dipole quantum memory

We present a quantum memory protocol for photons that is based on the direct control of the transition dipole moment. We focus on the case where the light-matter interaction is enhanced by a cavity. We show that the optimal write process (maximizing the storage efficiency) is related to the optimal read process by a reversal of the {\it effective time} $\tau=\int dt g^2(t)/\kappa$, where $g(t)$ is the time-dependent coupling and $\kappa$ is the cavity decay rate. We discuss the implementation of the protocol in a rare-earth ion doped crystal, where an optical transition can be turned on and off by switching a magnetic field.

Creation of quantum correlations between two atoms in a dissipative environment from an initial vacuum state

We have investigated the effect of counter-rotating terms on the dynamics of entanglement and quantum discord between two identical atoms interacting with a lossy single mode cavity field for a system initially in a vacuum state. The counter-rotating terms are found to lead to steady states in the long-time limit which can have high quantum discord, but have no entanglement. The effect of cavity decay rate on this steady-state quantum discord has been also investigated, surprisingly, the increase in cavity decay rate is found to enhance the steady-state quantum discord.

Anomalous ring-down effects and breakdown of the decay rate concept in optical cavities with negative group delay

The propagation of light pulses through negative group velocity media is known to give rise to a number of paradoxical situations that seem to violate causality. The solution of these paradoxes has triggered the investigation of a number of interesting and unexpected features of light propagation. Here, we report a combined theoretical and experimental study of the ring-down oscillations in optical cavities filled with a medium with a sufficiently negative frequency dispersion to give a negative round-trip group delay time. We theoretically anticipate that causality imposes the existence of additional resonance peaks in the cavity transmission, resulting in a non-exponential decay of the cavity field and in a breakdown of the cavity decay rate concept. Our predictions are validated by simulations and by an experiment using a room-temperature gas of metastable helium atoms in the detuned electromagnetically induced transparency regime as the cavity medium.

Stationary Inversion of a Two Level System Coupled to an Off-Resonant Cavity with Strong Dissipation

We present an off-resonant excitation scheme that realizes pronounced stationary inversion in a two level system. The created inversion exploits a cavity-assisted two-photon resonance to enhance the multiphoton regime of nonlinear cavity QED and survives even in a semiconductor environment, where the cavity decay rate is comparable to the cavity-dot coupling rate. Exciton populations of greater than 0.75 are obtained in the presence of realistic decays and pure dephasing. Quantum trajectory simulations and master equation calculations help elucidate the underlying physics and delineate the limitations of a simplified rate equation model. Experimental signatures of inversion and multiphoton cavity QED are predicted in the fluorescence intensity and second-order correlation function measured as a function of drive power.

Nonclassical Behavior of an Intense Cavity Field Revealed by Quantum Discord

We investigate the quantum-to-classical crossover of a dissipative cavity field by measuring the correlations between two noninteracting atoms coupled to the cavity mode. First, we note that there is a time window in which the mode shows a classical behavior, which depends on the cavity decay rate, the atom-field coupling strength, and the number of atoms. Then, considering the steady state of two atoms inside the cavity, we note that the entanglement between the atoms disappears while the mean number of photons of the cavity field (n) rises. However, the quantum discord reaches an asymptotic nonzero value even in the limit of n→∞, whether n is increased coherently or incoherently. Therefore, the cavity mode always preserves some quantum characteristics in the macroscopic limit, which is revealed by the quantum discord.

Few emitters in a cavity: from cooperative emission to individualization

We study the temporal correlations of the field emitted by an electromagnetic resonator coupled to a mesoscopic number of two-level emitters that are incoherently pumped by a weak external drive. We solve the master equation of the system for increasing number of emitters and as a function of the cavity quality factor, and we identify three main regimes characterized by well-distinguished statistical properties of the emitted radiation. For small cavity decay rates, the emission events are uncorrelated and the number of photons in the emitted field becomes larger than one, resembling the build-up of a laser field inside the cavity. At intermediate decay rates (as compared with the emitter–cavity coupling) and for a few emitters, the statistics of the emitted radiation is bunched and strikingly dependent on the parity of the number of emitters. The latter property is related to the cooperativity of the emitters mediated by their coupling to the cavity mode, and its connection with steady-state subradiance is discussed. Finally, in the bad cavity regime the typical situation of emission from a collection of individual emitters is recovered. We also analyze how the cooperative behavior evolves as a function of pure dephasing, which allows us to recover the case of a classical source made of an ensemble of independent emitters, similar to what is obtained for a very leaky cavity. State-of-the-art techniques of Q-switch of resonant cavities, allied with the recent capability of tuning single emitters in and out of resonance, suggest this system to be a versatile source of different quantum states of light.