Resonance Fluorescence in a Squeezed Vacuum

Abstract

Fluorescence from a coherently driven two-level atom that is damped by a squeezed vacuum is studied. We show that the mean atomic polarization depends on the relative phases of the squeezed vacuum and the coherent driving field. The fluorescent spectrum is calculated and shows several modifications over the spectrum for normal resonance fluorescence. In particular, the central peak of the Mollow triplet has a linewidth that depends on the phase of the driving field. For strong squeezing this peak can either be much narrower or much broader than the natural linewidth of the atom.     

Influence of squeezing bandwidths on resonance fluorescence

Abstract

We present an analytical technique for investigating the behaviour of a coherently driven atom damped by a squeezed vacuum with finite squeezing bandwidth. A master equation and analytic expressions for the fluorescent spectrum are derived for the simple case of a two-level atom exactly resonant with the frequencies of both the squeezed field and the driving field. Suitable choices of driving strength, phase and squeezing source lead to either sub-natural lincwidths of the Rabi sidebands or a sub-natural linewidth of the central spectral peak or indeed sub-natural linewidths of all three spectral peaks when squeezing bandwidths are taken into account. We also establish the remarkable result that in the strong driving regime, the width of the central peak of the fluorescent spectrum depends solely on the squeezing found at the Rabi sideband frequencies.     

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 the Binomial Field Distribution on Collapse and Revival Phenomena in the Jaynes-Cummings Model

Abstract

The dynamical properties of a two-level atom interacting with a single non-decaying mode of an electromagnetic field in a binomial state are studied. The statistical aspects of the field, such as intensity-intensity correlation and squeezing, are also investigated. The binomial state reduces to a pure number state and a pure coherent state in different limits. Hence it enables us to study how the sinusoidal Rabi oscillations in a pure number state develop to give rise to the phenomenon of collapse and revival which has been studied extensively in the coherent-state field. In addition, the binomial state exhibits squeezing for certain values of parameters, but it is not a minimum-uncertainty-product state.     

Generalized Bloch-Siegert Shift in a Squeezed Vacuum

Abstract

The time evolution of the atomic dipole moment of a two-level atom damped by an off-resonance squeezed vacuum is studied. Our results are valid for arbitrary detuning between the carrier frequency of the squeezed vacuum and the atomic transition frequency and show that the atomic dipole moment can oscillate with two dominant frequencies. These frequencies are shifted from their central values by an amount which is proportional to the degree of squeezing. We show that this shift of the frequencies is the exact equivalent of the optical Bloch-Siegert shift in the case of the ordinary vacuum damping without the rotating-wave approximation.     

Einstein localization in entangled light scattering

Abstract

We discuss Einstein-Podolsky-Rosen (EPR)-type entanglement in two-particle break-up, using Raman scattering with atom recoil as an example. The Schmidt number K is used as a measure of entanglement and the conditions to acquire high entanglement are obtained. We also illustrate the EPR conditional uncertainty in a situation where Δx Δp reaches a value much smaller than the Heisenberg limit.     

Light Squeezing in the Jaynes-Cummings Model with Intensity-dependent Coupling

Abstract

We have found that in the intensity-dependent-coupling Jaynes-Cummings model with the coherent radiation field light squeezing exhibits periodical revivals. The influence of the initial states of the atom on the squeezing of light is investigated in detail.     

Unraveling mirror properties in time-delayed quantum feedback scenarios

Abstract

We derive in the Heisenberg picture a widely used phenomenological coupling element to treat feedback effects in quantum optical platforms. Our derivation is based on a microscopic Hamiltonian, which describes the mirror-emitter dynamics based on a dielectric, a mediating fully quantized electromagnetic field and a single two-level system in front of the dielectric. The dielectric is modelled as a system of identical two-state atoms. The Heisenberg equation yields a system of describing differential operator equations, which we solve in the Weisskopf–Wigner limit. Due to a finite round-trip time between emitter and dielectric, we yield delay differential operator equations. Our derivation motivates and justifies the typical phenomenologicalassumed coupling element and allows, furthermore, a generalization to a variety of mirrors, such as dissipative mirrors or mirrors with gain dynamics.     

Cavity field tomography via atomic beam deflection

Abstract

We propose a set-up where a classical field interacts via a two-level atom with a quantized field in a resonator. Due to entanglement we can reconstruct all available information about the field by measuring the momentum distribution of the atom.     

Controlling decoherence of a two-level atom in a lossy cavity

Abstract

By use of external periodic driving sources, we demonstrate the possibility of controlling the coherent as well as the decoherent dynamics of a two-level atom placed in a lossy cavity. The control of the coherent dynamics is elucidated for the phenomenon of coherent destruction of tunnelling (CDT), i.e. the coherent dynamics of a driven two-level atom in a quantum superposition state can be brought practically to a complete standstill. We study this phenomenon for different initial preparations of the two-level atom. We then proceed to investigate the decoherence originating from the interaction of the two-level atom with a lossy cavity mode. The loss mechanism is described in terms of a microscopic model that couples the cavity mode to a bath of harmonic field modes. A suitably tuned external cw-laser field applied to the two-level atom slows down considerably the decoherence of the atom. We demonstrate the suppression of decoherence for two opposite initial preparations of the atomic state: a quantum superposition state as well as the ground state. These findings can be used to decrease the influence of decoherence in qubit manipulation processes.     

Entropy squeezing of a degenerate two-photon process with a nonlinear medium

Abstract

This paper presents new results on some aspects of the properties of the entropy squeezing in the time development of a degenerate two-photon of a single-mode interacting with a two-level system with a nonlinear medium. A general analytic expression for the density matrix is obtained on the basis of a Hamiltonian generalized in that it includes nonlinear effects and Stark shifts, by means of which we identify and numerically demonstrate the region of parameters where significantly large squeezing can be obtained. The influence of various parameters on the entropy squeezing are explored. It is shown that features of the entropy squeezing were influenced significantly by changing the nonlinear medium, Stark shift and the detuning. The results show that, certain amounts of the nonlinear effect yield the superstructure of atomic Rabi oscillation and changes the quasiperiod of the entropy evolution and atomic inversion.     

Two-level atom in a squeezed vacuum with finite bandwidth

Abstract

The resonance fluorescence of a two-level atom driven by a coherent laser field and damped by a finite bandwidth squeezed vacuum is analysed. We extend the Yeoman and Barnett technique to a non-zero detuning of the driving field from the atomic resonance and discuss the role of squeezing bandwidth and the detuning in the level shifts, widths and intensities of the spectral lines. The approach is valid for arbitrary values of the Rabi frequency and detuning but for the squeezing bandwidths larger than the natural line-width in order to satisfy the Markoff approximation. The narrowing of the spectral lines is interpreted in terms of the quadrature-noise spectrum. We find that, depending on the Rabi frequency, detuning and the squeezing phase, different factors contribute to the line narrowing. For a strong resonant driving field there is no squeezing in the emitted field and the fluorescence spectrum exactly reveals the noise spectrum. In this case the narrowing of the spectral lines arises from the noise reduction in the input squeezed vacuum. For a weak or detuned driving field the fluorescence exhibits a large squeezing and, as a consequence, the spectral lines have narrowed linewidths. Moreover, the fluorescence spectrum can be asymmetric about the central frequency despite the symmetrical distribution of the noise. The asymmetry arises from the absorption of photons by the squeezed vacuum which reduces the spontaneous emission. For an appropriate choice of the detuning some of the spectral lines can vanish despite that there is no population trapping. Again this process can be interpreted as arising from the absorption of photons by the squeezed vacuum. When the absorption is large it may compensate the spontaneous emission resulting in the vanishing of the fluorescence lines.     

The Interaction of Displaced Number State and Squeezed Number State Fields with Two-level Atoms

Abstract

The time-evolution of a single two-level atom in a single-mode high-Q cavity is sensitive to the quantum fluctuations of the cavity radiation field and to its photon statistics: this sensitivity is realizable experimentally in the Rydberg atom micromaser. We study the effects of the interaction of a two-level atom with two new non-classical radiation fields: the squeezed number state and the displaced number state realizable by nonlinear and linear transformations of field number states which have an initially precise occupation number. The time-varying field fluctuations caused by the atomic interaction are described using the Q-function quasi-probability.     

Emission Spectra of a Two-level Atom Under the Presence of Another Two-level Atom

Abstract

We investigate the spectrum of light emitted by a two-level atom interacting with another two-level atom inside an ideal cavity within the frame of generalized Jaynes-Cummings model. The influence of various ratios of the coupling constants of the atoms to the field on the spectrum of the emitted light is studied in detail for the case when the atoms are supposed to be initially in the excited state and the field in a Fock state as well as their superposition.     

Effective Dipole Squeezing in the Non-degenerate Two-photon Jaynes-Cummings Model with Superposition State Preparation

Abstract

Effective dipole squeezing in the non-degenerate two-photon Jaynes-Cummings model for atom and fields initially prepared in superposition of states is investigated. It is shown that the squeezing can be exhibited in certain periods of time but it cannot be achieved for atomic spontaneous radiation processes.     

On the Squeezing of Coherent States by the Multiphoton Jaynes-Cummings Hamiltonian with an Intensity-dependent Coupling

Abstract

The squeezing properties of the multiphoton Hamiltonian with intensity-dependent coupling are evaluated for the [xcirc] and [pcirc] _x quadratures, for the initial state of a coherent electromagnetic field and an atom in the ground state. Two measures of squeezing: the percentage of total squeezing and the squeezing time-period percentage, are introduced. Interesting squeezing properties with respect to [xcirc] are observed for real coherent states when the time evolution of the above measures and of the time-averaged squeezing are analysed. The multiphoton intensity-dependent coupling Hamiltonian is found to be almost independent of the specific powers of the annihilation and creation operators, as long as the sum of the powers is kept constant.     

Non-classical Features in the Three-level Jaynes-Cummings Model

Abstract

The eigenfunctions and eigenenergies of the system composed of a cascade three-level atom and bichromatic or monochromatic field with arbitrary detunings are presented. The development of the state vector of the system with arbitrary initial conditions is obtained. The development of the quantum fluctuations and the second-order coherence degree for the field is calculated. The dependence of the squeezing and antibunching on the detunings, initial intensities and initial squeezing is studied. The contribution of single-photon and two-photon transitions to, and the influence of, the a.c. Stark effect on the squeezing are discussed.     

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).     

Laser Interferometer Gravitational-wave Observatories: An Overview

Abstract

The quest to detect gravitational radiation is on the threshold of a new era. Technological developments in the 1980s have led to the point where it is now possible to design an instrument based on the Michelson interferometer which should not only be able to detect gravity waves but should function as an astronomical observatory. Stimulated by the need for a southern hemisphere facility, the Australian National University in collaboration with the University of Western Australia is poised to enter this exciting field. Here, we will briefly describe the principle of operation of these giant laser interferometers and examine performance limits imposed by the Heisenberg uncertainty principle.     

Population trapping with quantized fields in two-channel models of atomic excitation

Abstract

In this paper, we study several models of two-channel atomic excitation involving quantized fields and search for field states that result in the trapping of the atomic population in a single bare state. This trapping is a result of quantum interference between the two channels. We study the following models: a two-level atom resonantly interacting with two quantized field modes, a two-level atom with competing one and three photon transitions, and a Raman coupled model containing both Stokes and anti-Stokes fields. We find a great variety of trapping states of the field, some of the states being highly non-classical. The effects of dissipation on the stability of the trapping states are discussed and a method for generating some of the states is presented.