Interaction of Superpositions of Coherent States of Light with Two-level Atoms

Abstract

We investigate some of the basic features of the interaction of superpositions of coherent states of light with two-level atoms in the framework of the Jaynes-Cummings model. We compare the behaviour of the system in the case of having a coherent superposition state and a statistical mixture of coherent states as an initial field. We investigate the collapses and revivals of the atomic inversion by studying the evolution of the Q function of the cavity field. We also establish the connection between the purity of the field and the collapses and revivals of the atomic inversion.     

Population trapping in the Jaynes-Cummings model with a Kerr nonlinearity in the cavity

Abstract

An electromagnetic field state is found which maintains the population inversion of the atom stationary during the interaction with the field through a Jaynes-Cummings model (JCM) with a Kerr type nonlinearity in the cavity. The condition of stationarity of the population inversion includes the phase coupling of atomic dipole with the field. We have shown that the Kerr nonlinearity in the cavity field significantly modifies the photon statistics of the trapped field state through an intensity dependent detuning in the field compared to the normal JCM trapping state. We have also demonstrated the novel features of sub-Poissonian character and the squeezing of the trapped field state. The dynamics of the initial trapped field is studied in terms of squeezing and the Q-function.     

Cooperative Atomic Behaviour and Oscillator Formation in a Squeezed Vacuum

Abstract

Time-dependent (numerical) results are presented for super-radiant behaviour in the Dicke model of N _a = 2, 3 atoms in a broad band squeezed vacuum. This concerns the fluctuations and the intensity of the fluorescent radiation as well as the atomic population inversion of the system with atoms initially in an atomic coherent state. In the steady state, and in the N _a → ∞, we show that the ‘atomic’ Dicke model behaves like a ‘giant quantum oscillator’, in which the number of excited atoms asymptotically approaches the average number of photons in the resonant mode of the squeezed vacuum, just as in the thermally driven case.     

Effects of Atomic Coherence on Collapses and Revivals in the Binomial State of the Field

Abstract

The effects of the coherence between the states of a two-level atom on the phenomenon of collapses and revivals in an undamped binomial state of the electromagnetic field are investigated. It is found that the Rabi oscillations exhibit qualitatively different behaviour for different phases of coherence between the levels. This behaviour in the binomial state of the field is in contrast with that in a coherent state field, in which case the Rabi oscillations are qualitatively the same for all values of the coherence between the two atomic levels.     

Interaction of Squeezed Light with Two-level Atoms

Abstract

We investigate some of the fundamental features of the interaction of squeezed light with two-level atoms in the framework of the Jaynes-Cummings model. We start our analysis by calculating the collapses and revivals of the atomic inversion. We discuss the degree of purity of the field (given by the entropy) and its disentanglement from the atomic source. The connection with the evolution of the Q-function is also made. We notice that contrary to the coherent state case, the field turns into a nearly pure (squeezed) state at the revival time as if the field was prepared in a coherent state. The field also becomes a superposition of squeezed states at half of the revival time, and this is confirmed by investigating the photon number distribution. The phase properties of the field are discussed using the Pegg-Barnett formalism.     

The Jaynes-Cummings Model with a q Analogue of a Coherent State

Abstract

In this paper we study the time evolution of the atomic inversion of the two-level atom which is coupled to the q analogue of a single mode of the bosonic field. The q field under consideration is supposed to be prepared initially in the q analogue of Glauber's coherent state. We find that q deformation of Heisenberg algebra may correspond to some effective nonlinear interaction of the cavity mode.     

Effects of a Moving Mass Centre on Atomic Dynamics in Locally Inhomogeneous Quantized Cavity Field

Abstract

By invoking an exactly solvable model as the generalization of the Jaynes-Cummings model, the influence of spatial motion of atomic centre on the dynamics of a single-mode cavity-two-level atom system are studied for various initial conditions. These investigations show that the Doppler effect exercised by the motion of atom in a locally inhomogeneous cavity field can lead to the phenomenon of oscillation collapse and revival in the transition probability and the atomic population inversion.     

Atomic Dipole Dynamics in the Thermal Quantized Cavity Field

Abstract

We consider the resonant interaction of a two-level atom with a thermal state of the quantized field in a lossless cavity. Non-trivial dynamics of the atomic dipole moment and the field quadrature components arise if the atom is initially prepared in a coherent superposition of its upper and lower states. In particular, the initial thermal field state acquires a well defined phase that corresponds to the initial phase of the superposition atomic state. Population trapping occurs when the intensity grows.     

Atomic interference in the micromaser and statistical properties of the micromaser field

Abstract

In this paper we report on atomic interferometry in the micromaser. The atomic inversion is recorded while scanning the cavity frequency across the atomic resonance. For high pump rates, interference patterns are observed on the low-frequency wing of the maser line. The interferences are due to the non-adiabatic mixing of dressed states of the atoms at the entrance and exit holes of the maser cavity, leading to a Ramsey-type two-field interaction. Furthermore, statistical properties of the maser field are investigated via a measurement of the statistics of the pump atoms that leave the maser cavity. Theoretical expressions for the time dependence of the Fano–Mandel parameter Q _A(t) are compared with the experimental data. We demonstrate, that metastability of the maser field and atomic interference strongly influence the approach to a steady-state value of Q _A(t).     

N-level Atom Interacting with Single-mode Radiation Field: An Exactly Solvable Model with Multiphoton Transitions and Intensity-dependent Coupling

Abstract

We study the dynamics of an N-level atom coupled in a lossless cavity to a single-mode near-resonant quantized field. The atomic levels are coupled by the multiphoton transitions and the coupling constants between the field and the atomic levels are supposed to be intensity dependent. We find the exact solution for the state vector describing the dynamics of the atom-plus-field system. As an illustration we use the model for studying (i) the time evolution of the atomic occupation probability with the initially coherent field and (ii) the light squeezing, when the cavity field is initially in the vacuum state and the atom is prepared in the atomic ‘coherent state’ (a superposition of atomic states).     

Effect of quantum interference on a three-level atom driven by two laser fields

Abstract

We study the effect of quantum interference on the population distribution and absorptive properties of a V-type three-level atom driven by two lasers of unequal intensities and different angular frequencies. Three coupling configurations of the lasers to the atom are analysed: (a) both lasers coupled to the same atomic transition, (b) each laser coupled to different atomic transition and (c) each laser coupled to both atomic transitions. Dressed states for the three coupling configurations are identified, and the population distribution and absorptive properties of the weaker field are interpreted in terms of transition dipole moments and transition frequencies among these dressed states. In particular, we find that in the first two cases there is no population inversion between the bare atomic states, but the population can be trapped in a superposition of the dressed states induced by quantum interference and the stronger field. We show, that the trapping of the population, which results from the cancellation of transition dipole moments, does not prevent the weaker field to be coupled to the cancelled (dark) transitions. As a result, the weaker field can be strongly amplified on transparent transitions. In the case of each laser coupled to both atomic transitions the population can be trapped in a linear superposition of the excited bare atomic states leaving the ground state unpopulated in the steady state. Moreover, we find that the absorption rate of the weaker field depends on the detuning of the strong field from the atomic resonances and the splitting between the atomic excited states. When the strong field is resonant to one of the atomic transitions a quasi-trapping effect appears in one of the dressed states. In the quasi-trapping situation all the transition dipole moments are different from zero, which allows the weaker field to be amplified on the inverted transitions. When the strong field is tuned halfway between the atomic excited states, the population is completely trapped in one of the dressed states and no amplification is found for the weaker field.     

The Effect of Phase Fluctuation on Electromagnetically Induced Transparency,Inversionless Lasing and Refractive Index Enhancement in a Λ System

Abstract

The steady-state behaviour for a Λ-type, three-level atomic system has been analysed by taking into account the effect of the phase fluctuation. It is shown that, for a monochromatic driving field, even if the probe field is in resonance with the corresponding atomic transition, a large refraction index can still be generated; for a finite linewidth of the driving field, inversionless lasing and index enhancement tends to disappear. Furthermore, the linewidth prevents the transparency of the medium.     

Virtual Photons,Causality and Atomic Dynamics in Spontaneous Emission

Abstract

The time-dependent electric energy density surrounding a two-level atom fixed at r = 0 is studied, the atom being taken in its excited state at t = 0 and the field being initially in the vacuum state. The atom-field coupling includes both rotating and counter-rotating terms. The energy density of the spontaneously emitted field in the rotating wave approximation is shown to behave non-causally, while in the presence of the complete coupling it is shown to vanish outside a sphere of radius r = ct centred on the atom. The deviations of atomic dynamics from the exponential Wigner-Weisskopf behaviour during spontaneous decay are shown to be deeply influenced by the counter-rotating terms. It is concluded that the virtual photons induced by the counter-rotating terms in the atom-field coupling are essential in order to ensure causality and cannot be neglected in any accurate treatment of spontaneous emission.     

Entropy Evolution of the Bimodal Field Interacting with an Effective Two-level Atom Via the Raman Transition

Abstract

The properties of entropy evolution of the bimodal field interacting with an effective two-level atom via the Raman transition are studied. The influences of the initial average photon number and of the atomic coherence on the evolution of the bimodal field entropy are examined. It is shown that the bimodal field is in a pure state only under certain conditions in the early stages of time evolution and later tends to a statistical mixture state with maximum entropy values; the bimodal field remains strongly entangled with the atom.     

Permanently disentangled states of atom–field system via spontaneously generated coherence

Abstract

The effect of spontaneously generated coherence on evolution of the entanglement between a driven four-level Y-type atom and its spontaneous emission field is studied. We have shown that the atom will be entangled to its spontaneous emission field due to spontaneously generated coherence and coherent population trapping at the steady state. It is found that the degree of entanglement strongly depends on the initial atomic state. So, it can be controlled by the pumping laser pulses used for preparing an initial atomic system. More interestingly, the atom–field system can be found in a permanently disentangled state for a properly prepared atom.     

Periodic Squeezing in the Tavis-Cummings Model

Abstract

By utilizing our previous operator solution [17], we have investigated the squeezing in the radiation field of the Tavis-Cummings model (collective N ? 1 two-level atoms interacting with a resonant single cavity quantized mode). With field and atoms initially in coherent field state strong or weak and atomic coherent state (of few excited atoms), periodic time-dependent squeezing in the field and the macroscopic polarization is expressed in terms of Jacobian elliptic functions of the first kind. The statistical investigations are carried out for the quasiprobability distribution functions (Wigner function and Q function). The distribution function of the field quadrature has a variance less (greater) than that for a coherent state if this quadrature is squeezed (unsqueezed).     

Non-conditioned generation of Schrödinger cat states in a cavity

We investigate the dynamics of a two-level atom in a cavity filled with a nonlinear medium. We show that the atom-field detuning δ and the nonlinear parameter χ⁽³⁾ may be combined to yield a periodic dynamics, allowing the generation of almost exact superpositions of coherent states (Schrödinger cats). By analysing the atomic inversion and the field purity, we verify that any initial atom-field state is recovered at each revival time, and that a coherent field interacting with an excited atom evolves to a superposition of coherent states at each collapse time. We show that a mixed field state (statistical mixture of two coherent states) evolves towards an almost pure field state as well (Schrödinger cat). We discuss the validity of these results by using the field fidelity and the Wigner function.     

Quantum Optics with One Atom in an Optical Cavity

Abstract

The quantum mechanical master equation for a single two-level atom in a single-mode optical cavity is numerically solved in both the quantum and the semiclassical limits. The quantum limit of few cavity photons shows semiclassically forbidden behaviour such as steady state two-level population inversion. Qualitatively new fluorescent spectra, having sidebands broadened by the cavity interaction, also occur. The quantum theory of the single-atom laser with injected signal is presented. At the interface between its quantum and semiclassical dynamics we elucidate the signature of semiclassical limit cycles.     

Counter-rotating Contributions in the Jaynes-Cummings Model

Abstract

We present several perturbative approaches to the Jaynes-Cummings model of optical resonance with the counter-rotating terms included. We find that there exists a hitherto overlooked phase-dependence of the atomic inversion which is due to an interference between the rotating wave and counter-rotating contributions.