Dependence of the evolution of the cavity radiation of a coherently pumped correlated emission laser on dephasing and phase fluctuation

Analysis of the dynamics of the cavity radiation of a coherently pumped correlated emission laser is presented. The phase fluctuation and dephasing are found to affect the time evolution of the two-mode squeezing and intensity of the cavity radiation significantly. The intensity and degree of the two-mode squeezing increase at early stages of the process with time, but this trend changes rapidly afterwards. It is also shown that they increase with phase fluctuation and dephasing in the strong driving limit, however the situation appears to be opposite in the weak driving limit. This essentially suggests that the phase fluctuation and dephasing weaken the coherence induced by a strong driving mechanism so that the spontaneous emission gets a chance. The other important aspect of the phase fluctuation, in this regard, is the relaxation of the time at which the maximum squeezing is manifested as well as the time in which the radiation remains in a squeezed state.Comment: 10 pages, 12 figure

Two-mode entanglement in two-component Bose-Einstein condensates

We study the generation of two-mode entanglement in a two-component Bose-Einstein condensate trapped in a double-well potential. By applying the Holstein-Primakoff transformation, we show that the problem is exactly solvable as long as the number of excitations due to atom-atom interactions remains low. In particular, the condensate constitutes a symmetric Gaussian system, thereby enabling its entanglement of formation to be measured directly by the fluctuations in the quadratures of the two constituent components [Giedke {\it et al.}, Phys. Rev. Lett. {\bf 91}, 107901 (2003)]. We discover that significant two-mode squeezing occurs in the condensate if the interspecies interaction is sufficiently strong, which leads to strong entanglement between the two components.Comment: 22 pages, 4 figure

Number operator-annihilation operator uncertainty as an alternative of the number-phase uncertainty relation

We consider a number operator-annihilation operator uncertainty as a well behaved alternative to the number-phase uncertainty relation, and examine its properties. We find a formulation in which the bound on the product of uncertainties depends on the expectation value of the particle number. Thus, while the bound is not a constant, it is a quantity that can easily be controlled in many systems. The uncertainty relation is approximately saturated by number-phase intelligent states. This allows us to define amplitude squeezing, connecting coherent states to Fock states, without a reference to a phase operator. We propose several setups for an experimental verification.Comment: 8 pages including 3 figures, revtex4; v2: typos corrected, presentation improved; v3: presentation considerably extended; v4: published versio

Mach-Zehnder Interferometry at the Heisenberg Limit with coherent and squeezed-vacuum light

We show that the phase sensitivity $\Delta \theta$ of a Mach-Zehnder interferometer fed by a coherent state in one input port and squeezed-vacuum in the other one is i) independent from the true value of the phase shift and ii) can reach the Heisenberg limit $\Delta \theta \sim 1/N_T$, where $N_T$ is the average number of particles of the input states. We also show that the Cramer-Rao lower bound, $\Delta \theta \propto 1/ \sqrt{|\alpha|^2 e^{2r} + \sinh^2r}$, can be saturated for arbitrary values of the squeezing parameter $r$ and the amplitude of the coherent mode $|\alpha|$ by a Bayesian phase inference protocol.Comment: 4 pages, 4 figure

Cardiovascular System Studies

Contains research objectives and reports on one research project.National Institutes of Health (Grant 5 TI HE 5550-03

On the Quantum Phase Operator for Coherent States

In papers by Lynch [Phys. Rev. A41, 2841 (1990)] and Gerry and Urbanski [Phys. Rev. A42, 662 (1990)] it has been argued that the phase-fluctuation laser experiments of Gerhardt, B\"uchler and Lifkin [Phys. Lett. 49A, 119 (1974)] are in good agreement with the variance of the Pegg-Barnett phase operator for a coherent state, even for a small number of photons. We argue that this is not conclusive. In fact, we show that the variance of the phase in fact depends on the relative phase between the phase of the coherent state and the off-set phase $\phi_0$ of the Pegg-Barnett phase operator. This off-set phase is replaced with the phase of a reference beam in an actual experiment and we show that several choices of such a relative phase can be fitted to the experimental data. We also discuss the Noh, Foug\`{e}res and Mandel [Phys.Rev. A46, 2840 (1992)] relative phase experiment in terms of the Pegg-Barnett phase taking post-selection conditions into account.Comment: 8 pages, 8 figures. Typographical errors and misprints have been corrected. The outline of the paper has also been changed. Physica Scripta (in press

Decoherence due to three-body loss and its effect on the state of a Bose-Einstein condensate

A Born-Markov master equation is used to investigate the decoherence of the state of a macroscopically occupied mode of a cold atom trap due to three-body loss. In the large number limit only coherent states remain pure for times longer than the decoherence time: the time it takes for just three atoms to be lost from the trap. For large numbers of atoms (N>10^4) the decoherence time is found to be much faster than the phase collapse time caused by intra-trap atomic collisions

Cardiovascular System Studies

Contains reports on two research projects.National Institutes of Health (Grant 5T1 HE 5550-02

Fidelity and the communication of quantum information

We compare and contrast the error probability and fidelity as measures of the quality of the receiver's measurement strategy for a quantum communications system. The error probability is a measure of the ability to retrieve classical information and the fidelity measures the retrieval of quantum information. We present the optimal measurement strategies for maximizing the fidelity given a source that encodes information on the symmetric qubit-states

Lyapunov exponent of the random frequency oscillator: cumulant expansion approach

We consider a one-dimensional harmonic oscillator with a random frequency, focusing on both the standard and the generalized Lyapunov exponents, $\lambda$ and $\lambda^\star$ respectively. We discuss the numerical difficulties that arise in the numerical calculation of $\lambda^\star$ in the case of strong intermittency. When the frequency corresponds to a Ornstein-Uhlenbeck process, we compute analytically $\lambda^\star$ by using a cumulant expansion including up to the fourth order. Connections with the problem of finding an analytical estimate for the largest Lyapunov exponent of a many-body system with smooth interactions are discussed.Comment: 6 pages, 4 figures, to appear in J. Phys. Conf. Series - LAWNP0