Quantum Optical Model Research Articles

Jaynes-Cummings models with trapped electrons on liquid helium

Jaynes-Cummings model is a typical model in quantum optics and has been realized with various physical systems (e.g, cavity QED, trapped ions, and circuit QED etc..) of two-level atoms interacting with quantized bosonic fields. Here, we propose a new implementation of this model by using a single classical laser beam to drive an electron floating on liquid Helium. Two lowest levels of the {\it vertical} motion of the electron acts as a two-level "atom", and the quantized vibration of the electron along one of the {\it parallel} directions, e.g., $x$-direction, serves the bosonic mode. These two degrees of freedom of the trapped electron can be coupled together by using a classical laser field. If the frequencies of the applied laser fields are properly set, the desirable Jaynes-Cummings models could be effectively realized.

Quantum forbidden-interval theorems for stochastic resonance

We extend the classical forbidden-interval theorems for a stochastic-resonance noise benefit in a nonlinear system to a quantum-optical communication model and a continuous-variable quantum key distribution model. Each quantum forbidden-interval theorem gives a necessary and sufficient condition that determines whether stochastic resonance occurs in quantum communication of classical messages. The quantum theorems apply to any quantum noise source that has finite variance or that comes from the family of infinite-variance alpha-stable probability densities. Simulations show the predicted noise benefits for the basic quantum communication model and the continuous-variable quantum key distribution model.

Cavity-QED models of switches for attojoule-scale nanophotonic logic

Quantum optical input-output models are described for a class of optical switches based on cavity quantum electrodynamics (QED) with a single multilevel atom (or comparable bound system of charges) coupled simultaneously to several resonant field modes. A recent limit theorem for quantum stochastic differential equations is used to show that such models converge to a simple scattering matrix in a type of strong-coupling limit that seems natural for nanophotonic systems. Numerical integration is used to show that the behavior of the prelimit model approximates that of the simple scattering matrix in a realistic regime for the physical parameters and that it is possible in the proposed cavity-QED configuration for low-power optical signals to switch higher-power signals at attojoule energy scales.

Deformed Clifford algebra and supersymmetric quantum mechanics on a phase space with applications in quantum optics

In order to realize supersymmetric quantum mechanics methods on a four-dimensional classical phase space, the complexified Clifford algebra of this space is extended by deforming it with the Moyal star product in composing the components of Clifford forms. Two isospectral matrix Hamiltonians having a common bosonic part but different fermionic parts depending on four real-valued phase-space functions are obtained. The Hamiltonians are doubly intertwined via matrix-valued functions which are divisors of zero in the resulting Moyal–Clifford algebra. Two illustrative examples corresponding to Jaynes–Cummings-type models of quantum optics are presented as special cases of the method. Their spectra, eigenspinors and Wigner functions as well as their constants of motion are also obtained within the autonomous framework of deformation quantization.

Coherent interference effects in a nano-assembled diamond NV center cavity-QED system

Diamond nanocrystals containing NV color centers are positioned with 100-nanometer-scale accuracy in the near-field of a high-Q SiO(2) microdisk cavity using a fiber taper. The cavity modified nanocrystal photoluminescence is studied, with Fano-like quantum interference features observed in the far-field emission spectrum. A quantum optical model of the system is proposed and fit to the measured spectra, from which the NV(-) zero phonon line coherent coupling rate to the microdisk is estimated to be 28 MHz for a nearly optimally placed nanocrystal.

Coherence transition of small Josephson junctions coupled to a single-mode resonant cavity: Connection to the Dicke model

We calculate the thermodynamic properties of a collection of N small Josephson junctions coupled to a single-mode resonant electromagnetic cavity, at finite temperature T, using several approaches. In the first approach, we include all the quantum-mechanical levels of the junction, but treat the junction-cavity interaction using a mean-field approximation developed previously for T = 0 . In the other approaches, the junctions are treated including only the two lowest energy levels per junction, but with two different Hamiltonians. The first of these maps onto the Dicke model of quantum optics. The second is a modified Dicke model which contains an additional XY-like coupling between the junctions. The modified Dicke model can be treated using a mean-field theory, which in the limit of zero XY coupling gives the solution of the Dicke model in the thermodynamic limit using Glauber coherent states to represent the cavity. In all cases, for an N-independent junction-cavity coupling, there is a critical junction number N above which there is a continuous transition from incoherence to coherence with decreasing T. If the coupling scales with N so as to give a well-behaved thermodynamic limit, there is a critical minimum coupling strength for the onset of coherence. In all three models, the cavity photon occupation numbers have a non-Bose distribution when the system is coherent.

Rabi Oscillations in Landau-Quantized Graphene

We investigate the relation between the canonical model of quantum optics, the Jaynes-Cummings Hamiltonian and Dirac fermions in quantizing magnetic field. We demonstrate that Rabi oscillations are observable in the optical response of graphene, providing us with a transparent picture about the structure of optical transitions. While the longitudinal conductivity reveals chaotic Rabi oscillations, the Hall component measures coherent ones. This opens up the possibility of investigating a microscopic model of a few quantum objects in a macroscopic experiment with tunable parameters.

Entanglements induced by cavity interacting with two-coupled atoms

We consider a quantum optics model where the cavity interacts with two-coupled atoms. The atom–atom entanglement, atoms–cavity entanglement and the mixture for the two atoms are investigated, and discuss the effects of the initial conditions, atom–atom coupling and the mean number of photons on the entanglements and mixture. We find that atom–atom coupling plays an important role in the entanglement and mixture. Numerical results show that under some conditions the phenomena of “entanglement sudden death” and “entanglement collapse and revival” emerge.

N+CPT clock resonance

In a typical compact atomic time standard a current modulated semiconductor laser is used to create the optical fields that interrogate the atomic hyperfine transition. A pair of optical sidebands created by modulating the diode laser become the coherent population trapping (CPT) fields. At the same time, other pairs of optical sidebands may contribute to other multiphoton resonances, such as three-photon N-resonance [Phys. Rev. A65, 043817 (2002)]. We analyze the resulting joint CPT and N-resonance (hereafter N+CPT) analytically and numerically. Analytically we solve a four-level quantum optics model for this joint resonance and perturbatively include the leading ac Stark effects from the five largest optical fields in the laser's modulation comb. Numerically we use a truncated Floquet solving routine that first symbolically develops the optical Bloch equations to a prescribed order of perturbation theory before evaluating. This numerical approach has, as input, the complete physical details of the first two excited-state manifolds of Rb87. We test these theoretical approaches with experiments by characterizing the optimal clock operating regimes.

Quantum Semi-Markov Processes

We construct a large class of non-Markovian master equations that describe the dynamics of open quantum systems featuring strong memory effects, which relies on a quantum generalization of the concept of classical semi-Markov processes. General conditions for the complete positivity of the corresponding quantum dynamical maps are formulated. The resulting non-Markovian quantum processes allow the treatment of a variety of physical systems, as is illustrated by means of various examples and applications, including quantum optical systems and models of quantum transport.

Intrinsic Decoherence Mechanisms in the Microcavity Polariton Condensate

The fundamental mechanisms which control the phase coherence of the polariton Bose-Einstein condensate (BEC) are determined. It is shown that the combination of number fluctuations and interactions leads to decoherence with a characteristic Gaussian decay of the first-order correlation function. This line shape, and the long decay times ( approximately 150 ps) of both first- and second-order correlation functions, are explained quantitatively by a quantum-optical model which takes into account interactions, fluctuations, and gain and loss in the system. Interaction limited coherence times of this type have been predicted for atomic BECs, but are yet to be observed experimentally.

Matter-wave squeezing and the generation ofSU(1,1)andSU(2)coherent states via Feshbach resonances

Pair operators for boson and fermion atoms generate $\text{SU}(1,1)$ and $\text{SU}(2)$ Lie algebras, respectively. Consequently, the pairing of boson and fermion atoms into diatomic molecules via Feshbach resonances, produces $\text{SU}(1,1)$ and $\text{SU}(2)$ coherent states, making bosonic pairing the matter-wave equivalent of parametric coupling and fermion pairing equivalent to the Dicke model of quantum optics. We discuss the properties of atomic states generated in the dissociation of molecular Bose-Einstein condensates into boson or fermion constituent atoms. The $\text{SU}(2)$ coherent states produced in dissociation into fermions give Poissonian atom-number distributions, whereas the $\text{SU}(1,1)$ states generated in dissociation into bosons result in super-Poissonian distributions, in analogy to two-photon squeezed states. In contrast, starting from an atomic gas produces coherent number distributions for bosons and super-Poissonian distributions for fermions.

Dynamics of the Jaynes–Cummings and Rabi models: old wine in new bottles

By using a wavepacket approach, this paper reviews the Jaynes–Cummings model with and without the rotating wave approximation (RWA) in a non-standard way. This gives new insight, not only of the two models themselves, but of the RWA as well. Expressing the models by field quadrature operators, instead of the typically used boson ladder operators, wavepacket simulations are presented. Several known phenomena of these systems, such as collapse-revivals, Rabi oscillation, squeezing and entanglement, are reviewed and explained in this new picture, either in an adiabatic or diabatic frame. The harmonic shape of the potential curves that the wavepackets evolve on and the existence of a level crossing make these results interesting in a broader sense not only for models in quantum optics, but especially in atomic and molecular physics.

Magnetic-flux-driven quantum phase transition in superconducting qubits coupled with a nanomechanical resonator

In this Brief Report, we investigate the collective quantum dynamics of a solid-state system containing a superconducting quantum interference device (SQUID) coupled with a nanomechanical resonator. When the charging energy is much larger than the Josephson energy, the SQUID can act as an artificial two-level atom near the degeneracy point. Thus, we theoretically realize the Dicke model in quantum optics. Furthermore, we predict that a superradiant phase transition for this model can be driven by an experimentally controllable external magnetic flux. The essential features of quantum criticality, such as the scaling behavior, critical exponent, and universality, are also given. Finally, we propose to observe this quantum phase transition by measuring the ground-state Berry phase.

Bistable spin currents from quantum dots embedded in a microcavity

We examine the spin current generated by quantum dots embedded in an optical microcavity. The dots are connected to leads, which allow electrons to tunnel into and out of the dot. The spin current is generated by spin flip transitions induced by a quantized electromagnetic field inside the cavity with one of the Zeeman states lying below the Fermi level of the leads and the other above. In the limit of strong Coulomb blockade, this model is analogous to the Jaynes-Cummings model in quantum optics. We find that the cavity field amplitude and the spin current exhibit bistability as a function of the laser amplitude, which is driving the cavity mode. Even in the limit of a single dot, the spin current and the Q distribution of the cavity field have a bimodal structure.

Spin current and shot noise from a quantum dot coupled to a quantized cavity field

We examine the spin current and the associated shot noise generated in a quantum dot connected to normal leads with zero bias voltage across the dot. The spin current is generated by spin flip transitions induced by a quantized electromagnetic field inside a cavity with one of the Zeeman states lying below the Fermi level of the leads and the other above. In the limit of strong Coulomb blockade, this model is analogous to the Jaynes-Cummings model in quantum optics. We also calculate the photon current and photon current shot noise resulting from photons leaking out of the cavity. We show that the photon current is equal to the spin current and that the spin current can be significantly larger than for the case of a classical driving field as a result of cavity losses. In addition to this, the frequency dependent spin (photon) current shot noise show dips (peaks) that are a result of the discrete nature of photons.

Dynamical properties of spin and subbands populations in 1D quantum wire

AbstractIn this paper we study the spin and subbands populations, as functions of time, for electrons in a quasi‐1D quantum wire, with spin–orbit coupling (SOC), to which a perpendicular magnetic field is applied. The system is governed by the Hamiltonian which, in the strong magnetic field limit, resembles the Jaynes–Cummings model (JCM) in quantum optics (QO). Using a procedure similar to that in QO, we explicitly present the time‐evolution operator, thereby calculating the spin states and subbands populations as functions of time. We show that the populations exhibit oscillations, depending on the interaction parameters, scale lengths and, particularly, the initial states of the system. Specifically, if the electrons are initially prepared in a maximal coherent superposition of spin states, the expectation values periodically collapse and revive. The collapse‐revivals are most profound for the spin along the magnetic field and subbands populations. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Quantization and asymptotic behaviour of [formula omitted] quantum random walk on integers

Quantization and asymptotic behaviour of a variant of discrete random walk on integers are investigated. This variant, the ε V k walk, has the novel feature that it uses many identical quantum coins keeping at the same time characteristic quantum features like the quadratically faster than the classical spreading rate, and unexpected distribution cutoffs. A weak limit of the position probability distribution (pd) is obtained, and universal properties of this arch sine asymptotic distribution function are examined. Questions of driving the walk are investigated by means of a quantum optical interaction model that reveals robustness of quantum features of walker's asymptotic pd, against stimulated and spontaneous quantum noise on the coin system.

Quantum-Noise-Initiated Symmetry Breaking of Spatial Solitons

The spectra of chi(2) spatial solitons are measured close to the soliton-formation threshold and show the presence of sidebands, shifted by 39 THz from the laser line. By comparing with the predictions of a quantum optical field model, solved numerically in the full (3 + 1)-dimensional space, it is claimed that the observed temporal instability of the spatial soliton is seeded by vacuum state fluctuations of the electromagnetic field.

Distributed entanglement in the two-photon two-mode non-linear process

In this paper we consider a quantum optics model where two-mode quantum light cavity with Kerr-like medium is coupled to an atom via two-photon process. The dynamical evolution of the system is studied in terms of entanglement measured by quantum relative entropy. The entanglements for the different bipartite partitions of the system, i.e., atom-two modes, mode-mode, mode-(atom+mode), are calculated explicitly and interesting trade-off relations between the different kinds of entanglement can be observed in different cases. The results show the entanglement between mode-mode is generally out of phase with that between atom and two modes, even though the two modes do not interact directly, and the Kerr-like medium prevents the atom and two modes from entangling.