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International Journal of Modern Physics B

ENTROPY OF A TWO LEVEL ATOM IN CONTACT WITH A SQUEEZED RESERVOIR

Robert R. Tucci

Published May 20, 1991• 13 citations
Publisher

Abstract

We study the entropy of a two level atom in contact with a non-minimum uncertainty squeezed reservoir and a coherent drive. Let δ be the phase of the coherent drive, and ΩR/γ the Rabi frequency divided by the atomic decay rate. For large, near minimum uncertainty squeezing, we find that the atomic quantum state is approximately a pure state, or, equivalently, a minimum entropy state, if ΩR/γ and δ satisfy (ΩR/γ)| cos δ| = 1/2. (Previous workers have only noted the occurrence of a pure state at δ = 0 or 180°.) We find that the atom saturates separately in each quadrature of the coherent drive. We also find that the thermodynamic order of the atom (given by the magnitude of the Bloch vector or by the negative of the atomic entropy) may increase as the background fluctuations or disorder increase. This behavior does not occur with non-squeezed reservoirs; it may be interpreted as a negative temperature effect, if atomic temperatures are defined in terms of the derivatives of the atomic entropy with respect to the variances of the two reservoir quadratures. We give an extensive collection of plots of the atomic entropy and temperatures. We find that a harmonic oscillator always cools down to lower temperatures than a 2 level atom if both bodies are in contact with the same squeezed reservoir.

DOI
10.1142/s0217979291000699

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We study the entropy of a two level atom in contact with a non-minimum uncertainty squeezed reservoir and a coherent drive. Let δ be the phase of the coherent drive, and ΩR/γ the Rabi frequency divided by the atomic decay rate. For large, near minimum uncertainty squeezing, we find that the atomic quantum state is approximately a pure state, or, equivalently, a minimum entropy state, if ΩR/γ and δ satisfy (ΩR/γ)| cos δ| = 1/2. (Previous workers have only noted the occurrence of a pure state at δ = 0 or 180°.) We find that the atom saturates separately in each quadrature of the coherent drive. We also find that the thermodynamic order of the atom (given by the magnitude of the Bloch vector or by the negative of the atomic entropy) may increase as the background fluctuations or disorder increase. This behavior does not occur with non-squeezed reservoirs; it may be interpreted as a negative temperature effect, if atomic temperatures are defined in terms of the derivatives of the atomic entropy with respect to the variances of the two reservoir quadratures. We give an extensive collection of plots of the atomic entropy and temperatures. We find that a harmonic oscillator always cools down to lower temperatures than a 2 level atom if both bodies are in contact with the same squeezed reservoir.
Squeezing of a two-level atom off-resonantly coupled to a non-Markovian reservoir is investigated. We compared two different definitions of squeezing that are based on the Heisenberg uncertainty relation and the entropy uncertainty relation and found that information entropy squeezing is more precise than variance squeezing as a measure of squeezing. Then we utilized entropy squeezing to examine the influences of the non-Markovian effect and detuning on the atomic squeezing. It is interesting to note that atomic squeezing can be protected for a long time when both the non-Markovian effect and detuning are present simultaneously. The physical mechanism is that the decay rate is suppressed much more by detuning in the non-Markovian regime than in the Markovian case.
We investigate a cavity mode that interacts with a three-level atom in an open cavity that is coupled to a vacuum reservoir and is driven by coherent light. In our analysis, the interaction of the three-level atom with the external vacuum reservoir is taken into account and the noise operators of the vacuum reservoir are placed in normal order. While the spontaneous emission rate fluctuates as [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], the cavity damping constant and stimulated emission decay constant, both set to 0.8, govern the system dynamics. Both the plus and negative components of the cavity light display quadrature squeezing. For coherent driving strengths [Formula: see text] and [Formula: see text] at [Formula: see text], and [Formula: see text] at [Formula: see text], the plus quadrature exhibits [Formula: see text] squeezing below the vacuum level, indicating that increasing the coherent drive can compensate for the decoherence introduced by spontaneous emission. Moreover, for [Formula: see text], the minus quadrature achieves [Formula: see text] squeezing. At high driving strengths, the squeezing in both quadratures becomes independent of spontaneous emission. In the absence of spontaneous emission, the mean photon number increases, and the photon number distribution shows a higher probability for even photon numbers than for odd ones, with the overall distribution decreasing as the photon number increases.
The analytical solution of the problem of two two-level atoms with degenerate two-photon transitions interacting with a single-mode radiation field in the presence of a parametric amplifier term is presented. The purity of the atomic state has been used to measure the degree of entanglement between the atom and the field. The temporal evolution of variance and entropy squeezing as well as atomic inversion for the single-atom case are studied. It has been shown that maximum squeezing for the variance and entropy squeezing occurs when the ratio between the amplifier coupling λ3 and the field frequency ω equals 0.26. Increasing the value of the ratio λ3/ω further leads to the vanishing of squeezing from the system. It is also noted that the existence of the coupling parameter results in the system never reaching the pure state except at the points of revival times. The Q function has been also considered to give more information in the phase space about the system. These aspects are sensitive to changes in the amplifier parameter.
We examine the impact of the non-Markovian environment on the dynamical behavior of the quantum coherence and entropy squeezing considering a two-level atomic system (qubit) immersed in a reservoir with zero-temperature for two types of non-Markovian environments. We consider a cavity little off-resonance with the transition frequency of the qubit and the case of a non-perfect photonic band gap (PBG). We show that the amount of coherence is dependent on the structure of the environment and influenced through the memory effects. We obtain that the delay and revival of the coherence loss might take place by controlling the detuning of the cavity-qubit system. Whereas, a partial coherence trapping occurs in non-ideal PBG and the decrease of the gap width will destroy the coherence. On the other hand, we show the situation for which the squeezing is occurring and enhanced with respect to the main parameters for the system. Finally, we display the monotonic dependence of the quantum coherence and squeezing on the main model parameters.
The master equation for a two-level atom interacting with a strong coherent field and damped into a reservoir formed by a finite bandwidth squeezed vacuum is derived. The master equation extends the Yeoman and Barnett approach to a non-zero detuning of the driving field from the atomic resonance and allows to discuss the role of squeezing bandwidth and the detuning in the level shifts, widths and intensities of spectral lines. The approach is valid for arbitrary values of the Rabi frequency and detuning but for the squeezing bandwidths larger than the natural linewidth in order to satisfy the Markov approximation.
Abstract We investigate the quantum statistical and squeezing properties of radiation generated by a coherently driven three-level laser system coupled to a squeezed vacuum reservoir. The analysis is carried out using c-number Langevin equations for normally ordered operator moments, allowing a transparent description of the interplay among atomic coherence, coherent driving, and reservoir-induced correlations. We show that significant quadrature squeezing can be achieved under appropriate conditions, with the degree of squeezing strongly influenced by the linear gain coefficient of the squeezed-vacuum reservoir, the strength of the coherent driving, and the initial atomic preparation. In particular, we find that maximal initial atomic coherence alone does not lead to squeezing in the absence of coherent driving, highlighting the essential role of phase-sensitive amplification. The results further reveal a shift of optimal squeezing toward lower values of the atomic coherence parameter and higher values of the driving strength as the gain and reservoir squeezing increase. In addition, we demonstrate the coexistence of strong quadrature squeezing with super-Poissonian photon statistics, reflecting the distinct roles of phase-sensitive and intensity fluctuations. The squeezing spectrum is also analyzed to provide frequency-resolved insight into noise suppression, directly relevant to homodyne-detection measurements. These findings clarify the trade-off between coherent excitation, which enhances phase-sensitive correlations, and photon population growth, which tends to increase intensity fluctuations, and they highlight parameter regimes where strong nonclassical effects can be realized under parameter regimes consistent with experimentally demonstrated cavity-QED and squeezed-light implementations.