Quantum Optical Model Research Articles

An Alternative Map from a 2 + 1 Dimensional Charged Dirac Oscillator in the Background of a Uniform Perpendicular Magnetic Field to a Quantum Optics Model

We propose an alternative map from the the 2-dimensional charged Dirac oscillator in the background of a uniform perpendicular magnetic field onto a quantum optics model which contains both Jaynes-Cummings (JC) and Anti-Jaynes-Cummings (AJC) interactions. Different from previous work, we only introduce one kind of phonons and realize a symmetrical competition which is controlled by the magnetic field. Furthermore, we find that this model behaves as a quantum phase transition when a dimensionless parameter crosses its critical value. Several characteristics of quantum phase transition are exhibited explicitly.

Dicke-type phase transition in a spin-orbit-coupled Bose-Einstein condensate.

Spin-orbit-coupled Bose-Einstein condensates (BECs) provide a powerful tool to investigate interesting gauge field-related phenomena. Here we study the ground state properties of such a system and show that it can be mapped to the well-known Dicke model in quantum optics, which describes the interactions between an ensemble of atoms and an optical field. A central prediction of the Dicke model is a quantum phase transition between a superradiant phase and a normal phase. We detect this transition in a spin-orbit-coupled BEC by measuring various physical quantities across the phase transition. These quantities include the spin polarization, the relative occupation of the nearly degenerate single-particle states, the quantity analogous to the photon field occupation and the period of a collective oscillation (quadrupole mode). The applicability of the Dicke model to spin-orbit-coupled BECs may lead to interesting applications in quantum optics and quantum information science.

Spontaneous quantum emission from analog white holes in a nonlinear optical medium

A microscopic quantum-optical model is used to compute the spectrum of quantum vacuum emission from strong laser pulses propagating in nonlinear optical media, highlighting similarities and differences with respect to the emission of analog white holes as predicted by quantum field theory in curved spacetime.

On the Chirality Quantum Phase Transition of the Dirac Oscillator

Dirac oscillator subjects to an external magnetic field is re-examined. We show that this model can be mapped onto different quantum optics models if one insists to introduce two kinds of phonons which associate with the excitations of Dirac oscillator and magnetic field respectively. The conclusion about chirality quantum phase transition in the paper “Chirality quantum phase transition in the Dirac oscillator” (Bermudez et al. Phys. Rev. A, 77, 063815 2008) is only valid for a specific mapped quantum optics models rather than the Dirac oscillator itself. Thus, the conclusions about chirality quantum phase transitions in this paper are not universal.

Two-level system with broken inversion symmetry coupled to a quantum harmonic oscillator

We study the generalized Jaynes-Cummings model of quantum optics at the inversion-symmetry-breaking and in the ultrastrong coupling regime. With the help of a generalized multiphoton rotating-wave approximation, we study the stationary solutions of the Schr\"{o}dinger equation. It is shown that the problem is reduced to resonant interaction of two position-displaced harmonic oscillators. Explicit expressions for the eigenstates and eigenvalues of generalized Jaynes-Cummings Hamiltonian are presented. We exemplify our physical model with analytical and numerical considerations regarding collapse and revivals of the initial population of a two-level system and photon distribution function at the direct multiphoton resonant coupling.

A classical simulation of nonlinear Jaynes–Cummings and Rabi models in photonic lattices

The interaction of a two-level atom with a single-mode quantized field is one of the simplest models in quantum optics. Under the rotating wave approximation, it is known as the Jaynes-Cummings model and without it as the Rabi model. Real-world realizations of the Jaynes-Cummings model include cavity, ion trap and circuit quantum electrodynamics. The Rabi model can be realized in circuit quantum electrodynamics. As soon as nonlinear couplings are introduced, feasible experimental realizations in quantum systems are drastically reduced. We propose a set of two photonic lattices that classically simulates the interaction of a single two-level system with a quantized field under field nonlinearities and nonlinear couplings as long as the quantum optics model conserves parity. We describe how to reconstruct the mean value of quantum optics measurements, such as photon number and atomic energy excitation, from the intensity and from the field, such as von Neumann entropy and fidelity, at the output of the photonic lattices. We discuss how typical initial states involving coherent or displaced Fock fields can be engineered from recently discussed Glauber-Fock lattices. As an example, the Buck-Sukumar model, where the coupling depends on the intensity of the field, is classically simulated for separable and entangled initial states.

Two-photon-counting interferometry

Two-photon-counting interferometry has been realized by measuring the electrical current due to two-photon absorption in the space-charge layer of a semiconductor detector located at the output port of an interferometer. We apply this technique to study the correlation properties of twin beams issued from parametric fluorescence. We describe in detail how the different second-order correlation functions (interbeam, intrabeam) can be extracted at the femtosecond time scale from raw data. The values of these correlation functions determined by our experiments are in excellent agreement with theory. More precisely, extrabunching in twin beams is unambiguously demonstrated and theoretically described using two models: a comprehensive multimode quantum optics model and a simpler classical stochastic approach. Given the high brightness of our twin-beam source, both theories yield similar results. Finally, convenient analytical expressions of the correlation functions were derived from both theories, expressions in which we have been able to relate specific terms to accidental and exact coincidences between photons. Two-photon interferometry thus determines to which extent twin photons are twin. This technique should become a useful tool for future quantum optics developments.

Fisher information, Rényi entropy power and quantum phase transition in the Dicke model

Fisher information, Rényi entropy power and Fisher–Rényi information product are presented for the Dicke model. There is a quantum phase transition in this quantum optical model. It is pointed out that there is an abrupt change in the Fisher information, Rényi entropy power, the Fisher, Shannon and Rényi lengths at the transition point. It is found that these quantities diverge as the characteristic length: |λc−λ|−1/4 around the critical value of the coupling strength λc for any value of the parameter β.

Effect of thermal excitations of the reservoir on phase bistability in the fundamental model of quantum optics

The effect of the finite temperature of the reservoir on the phase bistability in the fundamental model of quantum optics is studied based on the Q distribution function calculated numerically and on the P distribution function obtained analytically in the case of large Rabi frequencies. The condition for the appearance of the phase bistability in a system with allowance for thermal excitations of the reservoir is obtained.

Nonlinearity in single photon detection: modeling and quantum tomography

Single Photon Detectors are integral to quantum optics and quantum information. Superconducting Nanowire based detectors exhibit new levels of performance, but have no accepted quantum optical model that is valid for multiple input photons. By performing Detector Tomography, we improve the recently proposed model [M.K. Akhlaghi and A.H. Majedi, IEEE Trans. Appl. Supercond. 19, 361 (2009)] and also investigate the manner in which these detectors respond nonlinearly to light, a valuable feature for some applications. We develop a device independent model for Single Photon Detectors that incorporates this nonlinearity.

Nonlinear interferometry approach to photonic sequential logic

Motivated by rapidly advancing capabilities for extensive nanoscale patterning of optical materials, I propose an approach to implementing photonic sequential logic that exploits circuit-scale phase coherence for efficient realizations of fundamental components such as a NAND-gate-with-fanout and a bistable latch. Kerr-nonlinear optical resonators are utilized in combination with interference effects to drive the binary logic. Quantum-optical input-output models are characterized numerically using design parameters that yield attojoule-scale energy separation between the latch states.

Rényi entropy and quantum phase transition in the Dicke model

The Rényi entropies of the Dicke model are presented. This quantum-optical model describes a single-mode bosonic field interacting with an ensemble of N two-level atoms. There is a quantum phase transition in the N→∞ limit. It is shown that there is an abrupt change in the Rényi entropy of order β at the transition point. Around the critical value of the coupling strength λc the Rényi entropy is proportional to the logarithm of the characteristic length and diverges as ln|λc−λ| for any order β. The pseudocapacity defined here in analogy with the heat capacity exhibits the phase transition. The critical exponent for the Dicke model is found to be 1 for any value of the parameter β.

Coherent-feedback control strategy to suppress spontaneous switching in ultralow power optical bistability

An optical resonator with intracavity Kerr nonlinearity can exhibit dispersive bistability suitable for all-optical switching. With nanophotonic elements it may be possible to achieve attojoule switching energies, which would be very attractive for ultralow power operation but potentially problematic because of quantum fluctuation-induced spontaneous switching. In this letter I derive a quantum-optical model of two Kerr-nonlinear ring resonators connected in a coherent-feedback loop and show via numerical simulation that a properly designed “controller” cavity can significantly reduce the spontaneous switching rate of a bistable “plant” cavity in a completely embedded and autonomous manner.

Excited-state phase transition and onset of chaos in quantum optical models

We study the critical behavior of excited states and its relation to order and chaos in the Jaynes-Cummings and Dicke models of quantum optics. We show that both models exhibit a chain of excited-state quantum phase transitions demarcating the upper edge of the superradiant phase. For the Dicke model, the signatures of criticality in excited states are blurred by the onset of quantum chaos. We show that the emergence of quantum chaos is caused by the precursors of the excited-state quantum phase transition.

The Dicke model in quantum optics: Dicke model revisited

A short review of recent developments of the Dicke model in quantum optics is presented. The focus is on the model in a cavity at zero temperature and in the rotating wave approximation. Topics discussed include spectroscopic structures, the giant quantum oscillator, entanglement and phase transitions.

Nonlinear phenomena, optical and quantum solitons

Research in the theory of solitons and its applications has undergone impressive development in recent years and has affected a broad range of fields, including theory of special functions, quantum integrable systems, numerical analysis, cellular automata, representations of quantum groups and

Energy spectra for quantum wires and two-dimensional electron gases in magnetic fields with Rashba and Dresselhaus spin-orbit interactions

We introduce an analytical approximation scheme to diagonalize parabolically confined two dimensional electron systems with both the Rashba and Dresselhaus spin-orbit interactions. The starting point of our perturbative expansion is a zeroth-order Hamiltonian for an electron confined in a quantum wire with an effective spin-orbit induced magnetic field along the wire, obtained by properly rotating the usual spin-orbit Hamiltonian. We find that the spin-orbit-related transverse coupling terms can be recast into two parts W and V, which couple crossing and non-crossing adjacent transverse modes, respectively. Interestingly, the zeroth-order Hamiltonian together with W can be solved exactly, as it maps onto the Jaynes-Cummings model of quantum optics. We treat the V coupling by performing a Schrieffer-Wolff transformation. This allows us to obtain an effective Hamiltonian to third order in the coupling strength k_Rl of V, which can be straightforwardly diagonalized via an additional unitary transformation. We also apply our approach to other types of effective parabolic confinement, e.g., 2D electrons in a perpendicular magnetic field. To demonstrate the usefulness of our approximate eigensolutions, we obtain analytical expressions for the n^th Landau-level g_n-factors in the presence of both Rashba and Dresselhaus couplings. For small values of the bulk g-factors, we find that spin-orbit effects cancel out entirely for particular values of the spin-orbit couplings. By solving simple transcendental equations we also obtain the band minima of a Rashba-coupled quantum wire as a function of an external magnetic field. These can be used to describe Shubnikov-de Haas oscillations. This procedure makes it easier to extract the strength of the spin-orbit interaction in these systems via proper fitting of the data.

Cavity QED treatment of interactions between a metal nanoparticle and a dipole emitter

We derive a full quantum optical model of interactions between a dipole and a metal nanoparticle. The electromagnetic field of the nanoparticle is quantized from the time-harmonic solution to the wave equation. We derive an analytical expression for the dipole-field coupling strength and the Purcell factor. The semiclassical theory, derived from the Maxwell-Bloch equations, is compared to the full quantum calculations based on numerical solution of the master equation. The metal nanoparticle-dipole system is found to be in an interesting regime of cavity quantum electrodynamics where dipole decay is dominated by dephasing, but the dipole-field coupling strength is still strong enough to achieve large cooperativity. In the presence of large dephasing, we show that simple semiclassical theory fails to predict the correct scattered field spectrum even in the weak-field limit. We reconcile this discrepancy by applying the random-phase-jump approach to the cavity photon number instead of the dipole operator. We also investigate the quantum fluctuations of the scattered field and show that they are significantly dependent on the dephasing rate.

Response of the Strongly Driven Jaynes-Cummings Oscillator

We analyze the Jaynes-Cummings model of quantum optics, in the strong-dispersive regime. In the bad-cavity limit and on time scales short compared to the atomic coherence time, the dynamics are those of a nonlinear oscillator. A steady-state nonperturbative semiclassical analysis exhibits a finite region of bistability delimited by a pair of critical points, unlike the usual dispersive bistability from a Kerr nonlinearity. This analysis explains our quantum trajectory simulations that show qualitative agreement with recent experiments from the field of circuit quantum electrodynamics.

A solution of the bosonic and algebraic Hamiltonians by using an AIM

We apply the notion of an asymptotic iteration method (AIM) to determine the eigenvalues of the bosonic Hamiltonians that include a wide class of quantum optical models. We consider the solutions of the Hamiltonians, which are even the polynomials of the fourth order with respect to the Boson operators. We also demonstrate the applicability of the method for obtaining the eigenvalues of the simple Lie algebraic structures. The eigenvalues of the multi-boson Hamiltonians have been obtained by transforming them into the form of the single boson Hamiltonian in the framework of the AIM.