Susskind-Glogower Phase Operator Research Articles

PHASE OPERATOR AND PHASE STATE IN THERMO FIELD DYNAMICS

We extend the Susskind–Glogower phase operator and phase state in quantum optics to thermo field dynamics (TFD). Based on the thermo entangled state representation, we introduce thermo excitation and de-excitation operators with which the phase operator and phase state in TFD can be constructed. The phase state treated as a limiting case of a new SU(1, 1) coherent states is also exhibited.

Infinite statistics and theSU(1, 1) phase operator

A few years ago, Agarwal (1991 Phys. Rev. A 44 8398) showed that the Susskind–Glogower phase operators, expressible in terms of Bose operators, provide a realization of the algebra for particles obeying infinite statistics. In this paper we show that the SU(1, 1) phase operators, constructed in terms of the elements of the su(1, 1) Lie algebra, also provide a realization of the algebra for infinite statistics. There are many realizations of the su(1, 1) algebra in terms of single or multimode bose operators, three of which are discussed along with their corresponding phase states. The Susskind–Glogower phase operator is a special case of the SU(1, 1) phase operator associated with the Holstein–Primakoff realization of su(1, 1).

Comment on Correlative amplitude-operational phase entanglement embodied by the EPR-pair eigenstate

In a recent paper in this journal Fan (Fan H 2002 J. Phys. A: Math. Gen.35 1007) discards the possibility of using a genuine phase-difference operator to investigate number-phase entanglement because of the lack of unitarity of the Susskind–Glogower phase operators. However, Fan overlooked the existence of a bona fide unitary operator exponential of the phase difference. Here we find the amplitude–phase maximally entangled states as the simultaneous eigenstates of the total number and the phase-difference operators.

ENTANGLEMENT OF AMPLITUDE AND OPTICAL PHASE INVOLVED IN THE EPR EIGENSTATE

By noticing that although single-mode Susskind–Glogower phase operator does not commute with photon number operator, two-mode nonlinear phase operator commutes with number-difference operator. We reveal that the common eigenstate <η| of two-particles' relative coordinate and total momentum involves the entanglement between phase and amplitude. We also reveal entanglement between number difference and amplitude inherent in the state |D,|η|>, where [Formula: see text] is a deductive state of |η>.

Atomic-dipole squeezing for arbitrarily prepared atom and field in multi-photon interaction

The atomic-dipole squeezing condition for arbitrarily prepared atomic and field states in multi-photon Jaynes-Cummings model was derived. Three special cases were discussed. For the field initially in a vacuum state and a certain eigenstate of the Susskind-Glogower phase operator, the analytical dipole squeezing conditions were obtained and the maximum squeezing values were calculated. For a squeezed vacuum input field, the dipole squeezing behaviours under the influence of the field squeezing parameterr and the phased atom were numerically treated.

Quantum phase superoperator and antinormal ordering of the Susskind-Glogower phase operators

The relations between the Susskind-Glogower phase operator and the quantum phase superoperator are discussed. It is shown that the quantum phase superoperators are closely related to the antinormal ordering of the Susskind-Glogower phase operators.

Boson Inverse Operators and a New Family of Two-photon Annihilation Operators

Abstract We introduce the inverse of the Hermitian operator (ââ †) and express the Boson inverse operators â −1 and â †−1 in terms of the operators â, â † and (ââ †)−1. We show that these Boson inverse operators may be realized by Susskind-Glogower phase operators. In this way, we find a new two-photon annihilation operator and denote it as â 2(ââ †)−1. We show that the eigenstates of this operator have interesting non-classical properties. We find that the eigenstates of the operators (ââ †)−1 â 2, â(ââ †)−1 â and â 2(ââ †)−1 have many similar properties and thus they constitute a family of two-photon annihilation operators.

Antinormally ordering of phase operators and the algebra of weak limits

We show that the antinormal ordering introduced for the Susskind-Glogower phase operators can be justified formally from the Pegg-Barnett Ψ-space formalism. The Susskind-Glogower operators are the weak limits on the infinite-dimensional Hilbert space H of the corresponding operators in the Pegg-Barnett formalism. Because the weak limit of a product of two sequences of operators is not necessarily the product of the respective weak limits of the two sequences it follows that the algebra of the Pegg-Barnett operators will not be preserved by their weak limits on H. However, we show that the antinormal ordering of the Susskind-Glogower operators is just what is required to preserve the algebra for the weak limits on H.

Antinormal ordering of Susskind-Glogower quantum phase operators.

A quantum phase description is developed by the use of the antinormal ordering of Susskind-Glogower phase operators. The theory is studied in the infinite-dimensional Hilbert space and it is closely related to the Pegg-Barnett quantum phase description in the finite-dimensional Hilbert space with a proper limiting procedure. Various applications of the antinormal ordering technique are presented.

Generalization of Susskind-Glogower Phase Operators and Inverse Field Operators to q-Deformed Case11The project supported in part by National Natural Science Foundation of China.

We analyze some properties of Susskind-Glogower (SG) phase operators and by making use of inverse field operators. The generalization of the analysis to q-deformed case is given.

Phase Resolution and Coherent Phase States

Abstract Various measures of phase resolution (including variance, entropy, confidence half-width, and reciprocal peak likelihood) are reviewed, and applied to the class of coherent phase states. These states arise naturally as eigenstates of the Susskind-Glogower phase operator, and are found to have near-optimal phase resolution properties for fixed mean photon number [nbar]. The mutual information for a communication channel based on coherent phase states is calculated as log ([nbar] + 1), within 1·5 bits of the theoretical maximum for single-mode channels.

Properties of the Measured Phase Operators in the Squeezed Number States

Abstract The phase properties of the squeezed number states have been studied from the lower order to the higher order via the measured phase operators (MPO) introduced by Barnett and Pegg and compared with those obtained via the Hermitian and Susskind-Glogower phase operators. We have found many new, interesting results. For the lower order, the phase fluctuations of the MPO are exactly independent of the photon number n. For the higher order, the corresponding fluctuations are a decreasing function of n.

Performance measures of quantum-phase measurement.

Dispersion and peak likelihood---two performance measures recently used for the description of quantum phase---are compared in this Rapid Communication. The Susskind-Glogower phase operator represents the extremal quantum estimator with respect to both measures. The states with infinite peak likelihood and zero phase information explicitly demonstrate that peak likelihood is not relevant to the phase measurement, whereas dispersion represents a well-behaved performance measure of the phase variable. Peak likelihood restricts the lower limit of the variance of photon number, and the above-mentioned states represent the extremal states of the Shapiro-Shepard [Phys. Rev. A 43, 3795 (1991)] uncertainty relation.

Population trapping in the Jaynes-Cummings model via phase coupling.

An expression for the population inversion in the Jaynes-Cummings model and the most general initial state of the atom-field system is presented. States that maintain the same level of population inversion when the atom and the field are initially decoupled are found. When the atom is prepared in a coherent superposition of its states and the field is in an eigenstate of the Susskind-Glogower phase operator, for a certain choice of the relative phase between the atomic dipole and the field, coherent trapping occurs. The evolution of the squeezing of the field for these states is given, and the dependence on the phase and on the mean photon number of the field is studied.

Phase fluctuations in the coherent light/anharmonic oscillator system via measured phase operators

Gerry has recently calculated the phase fluctuations in the coherent light/anharmonic oscillator system, using the standard Susskind-Glogower phase operator formalism. In the current work his calculations are redone in terms of the “measured phase operators” recently introduced by Barnett and Pegg. It is shown that this calculation is considerably easier, and unlike Gerry's work, gives closed forms while yielding results qualitatively similar to the standard formalism.