Squeezing with Rydberg Atoms

Abstract

It is shown that some 17 Rydberg Na atoms initially placed into a coherent atomic state and super-radiating into a low-Q microwave cavity at temperatures T ? 0·4 K will show modest squeezing in the fluorescence field, the squeezing arising from terms oscillating at twice the cavity frequency. It is also shown that similar numbers of Rydberg atoms undergoing resonance fluorescence in a coherent single-mode microwave driving field and without any cavity will show more substantial squeezing in the fluorescence field.     

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).     

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.     

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.     

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.     

Squeezing spectra from s -ordered quasiprobability distributions: application to dispersive optical bistability

It is well known that the squeezing spectrum of the field exiting a nonlinear cavity can be directly obtained from the fluctuation spectrum of normally ordered products of creation and annihilation operators of the cavity mode. In this article we show that the output field squeezing spectrum can be derived also by combining the fluctuation spectra of any pair of s -ordered products of creation and annihilation operators. The interesting result is that the spectrum obtained in this way from the linearized Langevin equations is exact, and this occurs in spite of the fact that no s -ordered quasiprobability distribution verifies a true Fokker–Planck equation; that is, the Langevin equations used for deriving the squeezing spectrum are not exact. The (linearized) intracavity squeezing obtained from any s -ordered distribution is also exact. These results are exemplified in the problem of dispersive optical bistability.     

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.     

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.     

Entanglement and Sudden Death for a Two-Mode Radiation Field Two Atoms

The effect of the field–field interaction on a cavity containing two qubit (TQ) interacting with a two mode of electromagnetic field as parametric amplifier type is investigated. After performing an appropriate transformation, the constants of motion are calculated. Using the Schrödinger differential equation a system of differential equations was obtained, and the general solution was obtained in the case of exact resonance. Some statistical quantities were calculated and discussed in detail to describe the features of this system. The collapses and revivals phenomena have been discussed in details. The Shannon information entropy has been applied for measuring the degree of entanglement (DE) between the qubits and the electromagnetic field. The normal squeezing for some values of the parameter of the field–field interaction is studied. The results showed that the collapses disappeared after the field–field terms were added and the maximum values of normal squeezing decrease when increasing of the field–field interaction parameter. While the revivals and amplitudes of the oscillations increase when the parameter of the field–field interaction increases. Degree of entanglement is partially more entangled with increasing of the field-field interaction parameter. The relationship between revivals, collapses and the degree of entanglement (Shannon information entropy) was monitored and discussed in the presence and absence of the field–field interaction.     

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).     

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.     

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.     

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.     

Entropy squeezing for a two-level atom

Abstract

The usual definition of squeezing, based on the Heisenberg uncertainty principle, measures uncertainty in terms of the standard deviation. It can run into difficulties when applied to squeezing in the two-level atom. An alternative definition of squeezing is presented for this system, based on information entropy theory, which overcomes the disadvantages of the definition based on the Heisenberg uncertainty relation. The utility of this definition is illustrated by examining squeezing in the information entropy of a two-level atom in the Jaynes-Cummings model, and in resonance fluorescence.     

Quantum Theory of Hyper-Raman Scattering

Abstract

We develop the quantum theory of stimulated hyper-Raman scattering (HRS) and discuss the quantum statistics of pump and Stokes fields. We show that the initially coherent pump field acquires a strong squeezing that exceeds the similar squeezing in other nonlinear processes also involving two-photon absorption. Stokes field statistics are analysed in detail as a function of the initial statistics of both modes. Bunching effects are shown to be amplified in the short-time region, while in asymptotics the antibunching of Stokes photons becomes dominant, which in many cases results in sub-Poissonian statistics of Stokes mode. We also find a number of correlation effects between the photons of the two modes.     

Pulsed single-mode laser in four-arm grazing incidence cavity

Abstract

A four-arm grazing-incidence cavity (GIC) is demonstrated. It ensures stable single-mode operation in a pulsed-laser system by interferometrically enhancing mode selection; the corresponding standard GIC operates on five modes. We compare the four-arm GIC with the standard GIC and with two other multiple-arm GICs and show that it gives the best overall performance in terms of mode selectivity and threshold. An analysis has been developed that allows cavity parameters to be optimized for mode selection. The analysis has been verified experimentally.     

Squeezing from Raman Scattering in Optical Parametric Oscillators

Abstract

The squeezing properties of the Raman scattering process which takes place when the lower output frequency from a non-degenerate optical parametric interaction approaches a resonance of the nonlinear medium placed inside an optical resonant cavity are presented. The linear stability analysis is performed and the spectrum for the output fields is given in terms of the quadrature phase components in the Wigner representation. Perfect squeezing for the amplitude difference between the output Stokes and anti-Stokes modes at the Hopf bifurcation point is obtained.     

Field-dipole orientation mechanism and higher order modes in atom guides

Abstract

In cavity quantum electrodynamics (CQED), cavity size, dipole position and dipole orientation are the main factors controlling cavity effects, for example, suppression and enhancement of spontaneous emission. However, the dynamical effects of dipole orientation in CQED have, to date, remained largely unexplored, with most treatments simply concentrating on two (or three) orthogonal directions to illustrate the variations of CQED effects with dipole orientation. No mechanism which determines the evolution of the dipole orientation has been put forward to describe typical situations where atoms move in the field of an excited cavity mode. We emphasize here that in the presence of a cavity mode, the average dipole orientation is automatically determined at every point to be parallel to the direction of the electric field vector of the cavity mode. Besides giving rise to a single value for the spontaneous emission rate, this mechanism is shown to have important consequences for the dynamics of atoms in atom guides. In particular, it determines the average trapping potential distributions and the average radiation forces which guide the atoms along a cylindrical cavity. The effects of the field-dipole orientation mechanism are illustrated with reference to typical situations involving sodium atoms in sub-micron cylindrical guides. The role of a higher order cavity mode of the cylinder in the dynamics is highlighted in terms of its influence on the rotational and vibrational motions in such guides.     

Production of Macroscopic Schrödinger Cat States from Weak Quantized Cavity Fields Interacting with Atoms Driven by Classical Fields

Abstract

We show that macroscopic superposition (Schrödinger cat) states of a quantized single-mode cavity field can be produced via the interaction of this field with a two-level atom which is driven by a classical field even for small initial intensities of the quantized cavity mode. We show that with a properly chosen driving field an almost pure superposition state with arbitrary amplitudes and phases of component states can be produced.     

Producing GHZ state of nitrogen-vacancy centers in cavity QED

Abstract

We propose a scheme to generate the GHZ state of nitrogen-vacancy centers coupled to a whispering-gallery mode cavity. The implemented evolution is independent of the cavity field state with the assistance of a strong classical field, and thus not sensitive to the thermal state of the cavity. Meanwhile, it is fast compared to the convectional dispersive interaction induced operation in a cavity-assisted system. The scheme is readily scalable to the multiqubit scenario.