Non-classical Properties of Two-mode SU(1, 1) Coherent States

Abstract

We examine the non-classical properties of two-mode coherent states based on different unitary irreducible representations of SU(1, 1). Such states are generated by the action of the two-mode squeezing operator on initial states of the field containing arbitrary numbers of photons in each of the two modes. If the initial state of the field is a two-mode vacuum state, the final state is of course the two-mode squeezed vacuum. An initial occupation generalizes the idea of a squeezed vacuum to the SU(1, 1) coherent states. We show that fields in such states have remarkable quantum properties such as sub-Poissonian statistics, violations of the Cauchy-Schwarz inequality, strong correlations in the photon number fluctuations and squeezing. Using information theory formalism, we show that these coherent states are less correlated than the usual two-mode squeezed vacuum. Moreover, we show that an initial coherent amplitude contribution, in a large amplitude limit, can result in the reduction of correlations between modes.     

SU(1,1) Squeezing of SU(1,1) Generalized Coherent States

Abstract

In this paper we have introduced a new class of the SU(1,1) coherent states which are the eigenstates of the generalized annihilation operator K_. We have also studied the SU(1,1) squeezing of the SU(1,1) generalized coherent states interacting with a nonlinear medium modelled as an anharmonic oscillator.     

SU(2) and SU(1,1) Rotation Transformation and Pseudo-vector Model in Quantum Optics

Abstract

We construct a pseudo-vector model and realize the rotation transformation for the SU(2) and SU(1,1) dynamics. We introduce concepts of the pseudo-scalar and the scalar product in quantum optics. Several equivalents of the SU(2) and SU(1,1) unified rotation operator are given. By using this method, the two- and three-level Jaynes-Cummings model is discussed in the non-rotating wave approximation.     

Collapse-revival Phenomenon in the Jaynes-Cummings Model Interacting with the Multiphoton Holstein-Primakoff SU(2) Coherent State

Abstract

We have analysed the behaviour of the atomic population inversion of the two-level atom interacting with a single-mode field initially prepared in the multiphoton Holstein-Primakoff SU(2) coherent state. It is shown that the behaviour of the atomic inversion depends on the parameters characterizing the initial state of the field. In particular, the atomic inversion can exhibit periodical oscillations as well as the collapse-revival phenomenon.     

Study of Hole Pair Condensation based on the SU(2) Slave-Boson Approach to the t-J Hamiltonian; Temperature, Momentum and Doping Dependences of Spectral Functions

Based on the U(1) and SU(2) slave-boson approaches to the t-J Hamil-tonian, we evaluate the one electron spectral functions for the hole doped high T _c cuprates for comparison with the angle resolved photoemission spectroscopy(ARPES) data. We find that the observed quasiparticle peak in the superconducting state is correlated with the hump which exists in the normal state. We find that the spectral weight of the quasiparticle peak increases as doping rate increases, which is consistent with observation. As a conse-quence of the phase fluctuation effects of the spinon and holon pairing order parameters the spectral weight of the predicted peak obtained from the SU(2) theory is found to be smaller than the one predicted from U(1) mean field theory.     

Two-mode Squeezed Pair Coherent States

Abstract

The properties of states generated by the application of the two-mode squeeze operator to the pair coherent states are studied. These states are the two-mode analogues of the single-mode squeezed states generated by the application of the single-mode squeeze operator to an ordinary coherent state. In the present case there are correlations between the modes and strong non-classical properties are to be expected. We study the statistical properties of the photon number distributions, squeezing, violations of the Cauchy-Schwartz inequality, quasiprobability distributions and the phase distributions.     

Reversible Z-E Isomerism and Pharmaceutical Implications for SU5416

ABSTRACT

SU5416 (Z-isomer), the first in its class of angiogenesis inhibitors, in solution converts to the E-isomer following light exposure and reverts to the Z-isomer in the dark. Kinetics of this Z-E isomerism in pharmaceutical media is reported. Analytical solutions need light protection at 5°C to maintain integrity. While E-isomer in light-exposed product increased to 0.9% in 24 hours, light-protected product showed no change (25°C, 18 months). Infusate studies indicated that < 1.9% E-isomer will be dosed to patients and would likely convert to the Z-isomer, following administration. This report implies Z-E isomerism in SU5416 is controllable with no limitations towards ensuring pharmaceutical product quality.     

Statistical Properties of the Even Binomial State

Abstract

In this paper we introduce the even binomal state, which interpolates between the even number state and the even coherent state. We consider the effect of this state on the Glauber second order correlation function. Both squeezing phenomena are discussed, i.e., normal squeezing and amplitude squared squeezing. The quasiprobability distribution functions (Wigner function and Q function) for such a state are also examined.     

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.     

Quantum limits for minimum-uncertainty (MU) angular momentum polarization squeezed states

It is shown that there are certain quantum limits to angular momentum minimum-uncertainty (MU) obtained by polarization squeezing Hamiltonians, beyond which the MU cannot be realized. The analysis is made for two cases: (a) when a strong coherent state is in one mode and a squeezed vacuum is in the other mode. (b) For the interference between two optical modes which are amplitude squeezed, with equal squeezing and intensities’ magnitudes.     

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).     

Stimulated Raman Scattering of Squeezed Light with Pump Depletion

Abstract

Using the approximation of small fluctuations around a stationary point, photon statistics and squeezing of vacuum fluctuations are derived in stimulated Raman scattering including the coupling of photon-photon and photon-phonon modes. The depletion of pump light is described and it is shown that a regime of inversion of the process is related to an increase in quantum fluctuations, which are finally reduced again, more in the anti-Stokes mode than in the Stokes mode. If the anti-Stokes coupling is stronger than the Stokes coupling, then an oscillating behaviour of the statistical characteristics occurs and substantial squeezing can be found in photon-phonon modes.     

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.     

Parametric oscillation with squeezed vacuum reservoirs

Employing the quantum Hamiltonian describing the interaction of a two-mode light (signal–idler modes) generated by a non-degenerate parametric oscillator (NDPO) with two uncorrelated squeezed vacuum reservoirs (USVR), we derive the master and the Fokker–Planck equations. The corresponding Fokker–Planck equation for the Q-function is then solved employing a propagator method developed by K. Fesseha [J. Math. Phys. 33 2179 (1992)]. Making use of this Q-function, we calculate the quadrature fluctuations of the optical system. From these results we infer that the signal–idler modes are in squeezed states. When the NDPO operates below threshold we show that, for a large squeezing parameter, a squeezing amounting to a noise suppression approaching 100% below the vacuum level in one of the quadratures can be achieved.     

Interaction of a System of Initially Unexcited Two-level Atoms with a Weak Cavity Field

Abstract

Using a perturbation method, constructed in terms of SU(2) group representations, the interaction of N initially unexcited two-level atoms and a weak single-mode cavity field is studied. The field is assumed to be initially either in a Fock state with a number of photons equal to n or in a coherent state. In the case of the photon-number state with n  3, the pure phenomenon of collective collapses and revivals manifests itself. For the initially coherent field the phenomenon of collapses and revivals arising from the photon number distribution mechanism is additionally modulated by this collective mechanism. The problem of the interaction of excited atoms with an initially coherent field has already been solved numerically by Barnett and Knight. For n=1 2 and 3 the approximate solution is compared with the exact solutions also given in this paper and the limit of applicability of our approach is established.     

Squeezing in Correlated Quantum Systems

Abstract

We discuss the connection between quantum correlations and squeezing in simple quantum optical systems. We illustrate this connection by a study of two-mode states of light produced by parametric down-conversion and similar two-photon processes. The intermode correlations in these systems are shown to be responsible for modifications in photon-number sum and difference operators, and for squeezing in the superpositions of the two modes. The disappearance of the diagonal coherent-state quasiprobability function P(α) when non-classical light properties are important is noted, and alternative and better-behaved Wigner functions and coherent-state expectation Q-functions for the two-mode system are developed.     

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.     

Hot Water Reuse (HWR) of Dialyzers Gives Smoother Dialysis than Single Use (SU) or Chemical Reuse (CRU)

Background:  Hemodialyzers can be used once or reused after treatment with chemicals or hot water. SU results in infusion of plastic compounds, particularly phthalic acid metabolites, into patients and chemical reuse releases formaldehyde, glutaraldehyde, or peracetic acid into the blood during dialysis.
Methods:  We studied the increase in pulse rate (PR) and fall in systolic and diastolic blood pressure (BP) and patients' subjective overall quality evaluation (OE) of dialysis (1 worst, 5 best) during 3706 daily dialyses in 23 patients. Fall in blood pressure and rise in PR during dialysis and overall quality evaluation were compared as patients changed from SU or chemical reuse to hot water reuse. During SU and chemical reuse, dialysis time was shorter (121 vs. 148 min), urea clearance higher (241 vs. 175 ml/min) but ultrafiltration lower (1.5 vs. 1.7 kg/dialysis) than during hot water reuse.
Results:  The results are summarized in the table.  

     

Scaling of decoherence effects in quantum computers

Abstract

The scaling of decoherence rates with qubit number N is studied for a simple model of a quantum computer in the situation where N is large. The two state qubits are localized around well-separated positions via trapping potentials and vibrational centre of mass motion of the qubits occurs. Coherent one and two qubit gating processes are controlled by external classical fields and facilitated by a cavity mode ancilla. Decoherence due to qubit coupling to a bath of spontaneous modes, cavity decay modes and to the vibrational modes is treated. A non-Markovian treatment of the short time behaviour of the fidelity is presented, and expressions for the characteristic decoherence time scales obtained for the case where the qubit/cavity mode ancilla is in a pure state and the baths are in thermal states. Specific results are given for the case where the cavity mode is in the vacuum state and gating processes are absent and the qubits are in (a) the Hadamard state (b) the GHZ state.     

Correlation and joint density matrix of two spatial–temporal modes from balanced-homodyne sampling

Abstract

A theoretical treatment is given which establishes dual-mode balanced-homodyne detection as a practical and well characterized technique for measuring optical field correlations, photon-number correlations, or the full quantum state of a pair of optical modes. The definition of modes used includes temporal wave packets, Gaussian or other beam profiles, or two-frequency fields. The proposed method allows the measurement of two-time correlations on sub-picosecond scales, the disentangling of the statistics of signal light in two spatially overlapping modes, and the measurement of field correlations, such as squeezing, over 100 THz bandwidths. We show how to estimate from the data the statistical errors on the measured correlations and the density matrix arising from finite data sets, and the errors introduced by using finite numbers of phases and relative amplitudes of the two local oscillator fields.