Single-mode Radiation Field Research Articles

Revivals and entanglement from initially entangled mixed states of a damped Jaynes-Cummings model

An exact density matrix of a phase-damped Jaynes - Cummings model (JCM) with entangled Bell-like initial states formed from a model two-state atom and sets of adjacent photon number states of a single mode radiation field is presented. The entanglement of the initial states and the subsequent time evolution is assured by finding a positive lower bound on the concurrence of local 2x2 projections of the full 2xinfinity JCM density matrix. It is found that the time evolution of the lower bound of the concurrence systematically captures the corresponding collapse and revival features in atomic inversion, relative entropies of atomic and radiation, mutual entropy, and quantum deficit. The atom and radiation subsystems exhibit alternating sets of collapses and revivals in a complementary fashion due to the initially mixed states of the atom and radiation employed here. This is in contrast with the result obtained when the initial state of the dissipationless system is a factored pure state of atom and radiation, where the atomic and radiation entropies are necessarily the same. The magnitudes of the entanglement lower bound and the atomic and radiation revivals become larger as both magnitude and phase of the Bell-like initial state contribution increases. The time evolution of the entropy difference of the total system and that of the radiation subsystem exhibits negative regions called "supercorrelated" states which do not appear in the atomic subsystem. Entangled initial states are found to enhance this supercorrelated feature. Finally, the effect of phase damping is to randomize both the subsystems for asymptotically long times .

Unitary realizations of the ideal phase measurement

We explicitly construct a large class of unitary transformations that allow to perform the ideal estimation of the phase-shift on a single-mode radiation field. The ideal phase distribution is obtained by heterodyne detection on two radiation modes after the interaction.

Effects of the radiation field on collapse and revival phenomena in a four-level system

The effect of the detuning on the collapse and revival of some quantum statistical properties, (such as mean photon number and Mandel's Q parameter), are investigated by considering the interaction of a four-level atomic system with a single-mode radiation field, when the atom is initially prepared in a coherent superposition of the upper excited state and the ground state and the field initially in a coherent state. It is found that, for off-resonance case, the detuning between the field and the atom has a significant influence on the collapse and revival phenomenon which leads to the emergence of collapse and revival with a small initial mean photon number n ̃ =1 . The revival time has been calculated. Numerical computations and discussion of the results are presented.

Generation of higher-order atomic dipole squeezing in a high- Q micromaser cavity. (II) Effect of nonlinear one-photon processes

In our preceding work (Physica A 246 (1997) 529), the concept of higher-order atomic dipole squeezing (HOADS) was introduced. In this paper, we discuss further the influence of the nonlinear interaction of a two-level atom with a single-mode radiation field via one-photon processes on the squeezing properties of higher-order quantum fluctuations in atomic dipole variables. Our numerical calculations demonstrate the importance of nonlinear one-photon processes for understanding the generation of higher-order squeezed states in a high- Q micromaser cavity. It is found that the nonlinear one-photon processes influence the stability, period, width, peak height and position of HOADS, which are significant in the development of higher-order correlation measurements in quantum optics and laser physics.

Quantum state preparation via asymptotic completeness

We demonstrate that any quantum state |chi> of a single mode radiation field can be prepared with arbitrarily high fidelity by interaction with a sequence of two-level atoms, prepared in a suitable initial state. No final state measurement of the atoms is needed.

State Preparation by Photon Filtering

We propose a setup capable of generating Fock states of a single mode radiation field. The scheme is based on coupling the signal field to a ring cavity through cross-Kerr phase modulation, and on conditional ON-OFF photodetection at the output cavity mode. The same setup allows to prepare selected superpositions of Fock states and entangled two-mode states. Remarkably, the detector's quantum efficiency does not affect the reliability of the state synthesis.

State Preparation by Photon Filtering

We propose a setup capable of generating Fock states of a single mode radiation field. The scheme is based on coupling the signal field to a ring cavity through cross-Kerr phase modulation, and on conditional ON-OFF photodetection at the output cavity mode. The same setup allows to prepare selected superpositions of Fock states and entangled two-mode states. Remarkably, the detector's quantum efficiency does not affect the reliability of the state synthesis.

Noise reduction in quantum tomography

We review the `adaptive tomography' technique, and study its application to the measurement of the field intensity and correlations, and to the reconstruction of the Wigner function of a single-mode radiation field. In both cases, this method strongly reduces statistical errors, thus making homodyne tomography a kind of low-noise universal detector.

STATE MEASUREMENT BY PHOTON FILTERING IN A RING CAVITY

We suggest a method for measuring the photon number distribution and the density matrix of a single-mode radiation field. The setup consists of a chain of active ring cavities, each fed by a strong coherent probe and coupled to the signal through cross-Kerr phase modulation. Each cavity is set at resonance by a different Fock component of the signal, so that the detection probability at the cavities output is proportional to the signal photon statistics. The off-diagonal elements of the density matrix can be evaluated by measuring the photon statistics of a set of displaced signal states. The suggested setup allows a reliable state measurement even with low quantum efficiency at detectors.

Sampling canonical phase distribution

represents the canonical phase distribution for the singlemode radiation field described by the density operator % @2#. The phase probability distribution of Eq. ~1! was earlier introduced by London @3#, and it also represents the limiting distribution of the truncation approach of Pegg and Barnett @4#. In addition, it has been independently derived by Helstrom @5# and Holevo @6# in the more general framework of quantum estimation theory. More recently, it has also been shown how to properly derive probability ~1! starting only from the correspondence principle and the Born statistical rule @7#. Finally, we mention that the probability ~1! represents the overlap between % , the state under examination, and the so-called Susskind-Glogower phase states @8#

THERMODYNAMICS OF A SUPERRADIANCE WITH A CLUSTER EXPANSION

N-atom single-mode radiation field interaction system is regarded as an interacting quasi-boson-photon system and is treated as a grand canonical ensemble.The explicit expression for the thermodynamical potential of the system is obtained using cluster expansion method.Some thermodynamic quantities are derived in terms of the general thermodynamic formulas.The numerical calculation and diagrams exhibit the thermodynamic behavior of the system.The singularities appearing in the critical line and other places furnish evidences of existence of the second kind of phase transformation in this collective system.

Linear response of a nonrelativistic hydrogenlike atom to a single-mode radiation field. I. Exact theory: The atomic ground state

Linear response of a nonrelativistic hydrogenlike atom to a single-mode radiation field. I. Exact theory: The atomic ground state

Linear response of a nonrelativistic hydrogenlike atom to a single-mode radiation field. II. Electric dipole approximation: General formalism

The interaction of a low-intensity laser field with a nonrelativistic one-electron atom is considered to the first order of perturbation theory and in the electric dipole approximation. The radiation field is turned on adiabatically modifying the initial unperturbed atomic state, which is either an angular-momentum eigenstate $|\mathrm{nlm}〉$ or a Stark state $|{\mathrm{nn}}_{e}m〉$. The first-order correction to the wave function is expressed both in the length and velocity gauges in terms of a vector function called the linear-response vector and depending on the field-free energy eigenstate. We derive in a unifying manner the linear-response vectors in the position representation, as closed-form contour integrals, starting from a unique generating function built up with the Coulomb Green function. The linear-response vectors are then evaluated in momentum space via a Fourier transformation: they are obtained as integral representations and also in explicit form, as generalized hypergeometric functions. With reference to the static limit, we complement earlier results and find the reduced linear-response vectors in momentum space, as Fourier transforms of their coordinate-representation counterparts. The low-frequency behavior of the length-gauge first-order correction to the ground-state wave function is established in coordinate as well as in momentum space. We finally point out the high-frequency limit of the linear response in the velocity gauge.

Generalized characteristic functions for a single-mode radiation field

We derive simple formulas for the higher-order moments of the quadrature operators operators of a two-field superposition by introducing a new generalized characteristic function depending on two complex variables. Using this formalism we investigate the preservation of higher-order squeezing during weak thermalization of an even coherent state.

Pólya states of quantized radiation fields, their algebraic characterization and non-classical properties

Polya states of single mode radiation field are proposed and their algebraic characterization and nonclassical properties are investigated. They degenerate to the binomial (atomic coherent) and negative binomial (Perelomov's su(1,1) coherent) states in two different limits and further to the number, the ordinary coherent and Susskind-Glogower phase states. The algebra involved turn out to be a two-parameter deformation of both su(2) and su(1,1). Nonclassical properties are investigated in detail.

Phase space distributions from three-port couplers

A wide class of phase space distributions of a single mode radiation field is shown to be directly accessible to measurement by linear symmetric three-port optical couplers.

Quantum-state homodyne measurement with vacuum ports.

We show that the quantum state of an N-mode light field can be reconstructed from the difference statistics recorded in multiport homodyning with N unused input ports. The theory is applied to balanced homodyne six-port detection, which is shown to be suited for measuring the Q function of a single-mode radiation field. \textcopyright{} 1996 The American Physical Society.

Theory of the two-photon micromaser: Linewidth.

In this paper, we study the linewidth of a two-photon micromaser by using an exact Hamiltonian approach. We consider a three-level atomic system interacting with a single-mode radiation field. The intermediate level is considered to be off resonant with the field. In this model, under the large detuning limit, two-photon transitions result. We calculate the linewidth of a two-photon micromaser and present results in the small and large detuning limits. In the small detuning limit, single-photon behavior is evident, whereas in the large detuning limit, true two-photon behavior is exhibited. We compare the results for the linewidth, under a large detuning limit, with the results obtained by using a phenomenological, effective Hamiltonian approach. The absence of the dynamic Stark shift in a phenomenological, effective Hamiltonian leads to qualitatively different results in the two approaches. \textcopyright{} 1996 The American Physical Society.

Effect of moving mass centre on the field entropy evolution and emission spectrum of an atom in an ideal ring cavity

Abstract The emission spectrum of a two-level atom with moving mass centre interacting with a single-mode radiation field in a ring cavity and the field entropy evolution has been studied. As a result, the theoretical curves of the emission spectrum have been given; the features of the emission spectrum depend not only on the photon statistical distribution of the initial field, such as the coherent field and the Fock state, but also on the bandpass width γ of the filter detector and distribution of mass-centre momentum. The properties of field entropy evolution show a damping function of time; it is different from that when the atom is at rest.

Quantum state measurement by realistic heterodyne detection.

The determination of the quantum properties of a single-mode radiation field by heterodyne or double homodyne detection is studied. The realistic case of not fully efficient photodetectors is considered. It is shown that a large amount of quite precise information is available, whereas the completeness of such information is also discussed. Some examples are given and the special case of states expressed as a finite superposition of number states is considered in some detail. \textcopyright{} 1996 The American Physical Society.