The linewidth of a non-Markovian atom laser

We present a fully quantum mechanical treatment of a single mode atom laser including pumping and output coupling. By ignoring atom-atom interactions, we have solved this model without making the Born-Markov approximation. We find substantially less gain narrowing than is predicted under that approximation.Comment: 4 pages, 1 encapsulated postscript figur

Adaptive Quantum Measurements of a Continuously Varying Phase

We analyze the problem of quantum-limited estimation of a stochastically varying phase of a continuous beam (rather than a pulse) of the electromagnetic field. We consider both non-adaptive and adaptive measurements, and both dyne detection (using a local oscillator) and interferometric detection. We take the phase variation to be \dot\phi = \sqrt{\kappa}\xi(t), where \xi(t) is \delta-correlated Gaussian noise. For a beam of power P, the important dimensionless parameter is N=P/\hbar\omega\kappa, the number of photons per coherence time. For the case of dyne detection, both continuous-wave (cw) coherent beams and cw (broadband) squeezed beams are considered. For a coherent beam a simple feedback scheme gives good results, with a phase variance \simeq N^{-1/2}/2. This is \sqrt{2} times smaller than that achievable by nonadaptive (heterodyne) detection. For a squeezed beam a more accurate feedback scheme gives a variance scaling as N^{-2/3}, compared to N^{-1/2} for heterodyne detection. For the case of interferometry only a coherent input into one port is considered. The locally optimal feedback scheme is identified, and it is shown to give a variance scaling as N^{-1/2}. It offers a significant improvement over nonadaptive interferometry only for N of order unity.Comment: 11 pages, 6 figures, journal versio

Phase measurements at the theoretical limit

It is well known that the result of any phase measurement on an optical mode made using linear optics has an introduced uncertainty in addition to the intrinsic quantum phase uncertainty of the state of the mode. The best previously published technique [H. M. Wiseman and R.B. Killip, Phys. Rev. A 57, 2169 (1998)] is an adaptive technique that introduces a phase variance that scales as n^{-1.5}, where n is the mean photon number of the state. This is far above the minimum intrinsic quantum phase variance of the state, which scales as n^{-2}. It has been shown that a lower limit to the phase variance that is introduced scales as ln(n)/n^2. Here we introduce an adaptive technique that attains this theoretical lower limit.Comment: 9 pages, 5 figures, updated with better feedback schem

Decoherence and Entanglement in Two-mode Squeezed Vacuum States

I investigate the decoherence of two-mode squeezed vacuum states by analyzing the relative entropy of entanglement. I consider two sources of decoherence: (i) the phase damping and (ii) the amplitude damping due to the coupling to the thermal environment. In particular, I give the exact value of the relative entropy of entanglement for the phase damping model. For the amplitude damping model, I give an upper bound for the relative entropy of entanglement, which turns out to be a good approximation for the entanglement measure in usual experimental situations.Comment: 5 pages, RevTex, 3 eps figure

Quantum-Noise Reduction in a Driven Cavity with Feedback

We show that amplitude-squeezed states may be produced by driving a feedback-controlled cavity with a coherent input signal. The feedback controls the transmissivity of one output from the cavity and is essentially equivalent to nonlinear absorption. The cavity effectively acts as a nonlinear reflector. Hence, amplitude-squeezed states with arbitrarily strong coherent intensities can be obtained

Squeezing based on nondegenerate frequency doubling internal to a realistic laser

We investigate theoretically the quantum fluctuations of the fundamental field in the output of a nondegenerate second harmonic generation process occuring inside a laser cavity. Due to the nondegenerate character of the nonlinear medium, a field orthogonal to the laser field is for some operating conditions indepedent of the fluctuations produced by the laser medium. We show that this fact may lead to perfect squeezing for a certain polarization mode of the fundamental field. The experimental feasibility of the system is also discussed.Comment: 6 pages, 5 figure

Effects of χ(3) nonlinearities in second-harmonic generation

We investigate the effects of higher-order, chi ((3)), nonlinearities on the process of second-harmonic generation. In the traveling-wave case we find substantive differences in the macroscopic behavior of the fields when the chi ((3)) components are present. In the intracavity cage, which has been investigated before using a Linearized analysis, we investigate regions where these analyses may not be valid, comparing and contrasting the full quantum simulations with previous results

Noise-free scattering of the quantized electromagnetic field from a dispersive linear dielectric

We study the scattering of the quantized electromagnetic field from a linear, dispersive dielectric using the scattering formalism for quantum fields. The medium is modeled as a collection of harmonic oscillators with a number of distinct resonance frequencies. This model corresponds to the Sellmeir expansion, which is widely used to describe experimental data for real dispersive media. The integral equation for the interpolating field in terms of the in field is solved and the solution used to find the out field. The relation between the in and out creation and annihilation operators is found which allows one to calculate the S-matrix for this system. In this model, we find that there are absorption bands, but the input-output relations are completely unitary. No additional quantum noise terms are required.Comment: Revtex, submitted to Physical Review

Theory of output coupling for trapped fermionic atoms

We develop a dynamic theory of output coupling, for fermionic atoms initially confined in a magnetic trap. We consider an exactly soluble one-dimensional model, with a spatially localized delta-type coupling between the atoms in the trap and a continuum of free-particle external modes. Two important special cases are considered for the confinement potential: the infinite box and the harmonic oscillator. We establish that in both cases a bound state of the coupled system appears for any value of the coupling constant, implying that the trap population does not vanish in the infinite-time limit. For weak coupling, the energy spectrum of the outgoing beam exhibits peaks corresponding to the initially occupied energy levels in the trap; the height of these peaks increases with the energy. As the coupling gets stronger, the energy spectrum is displaced towards dressed energies of the fermions in the trap. The corresponding dressed states result from the coupling between the unperturbed fermionic states in the trap, mediated by the coupling between these states and the continuum. In the strong-coupling limit, there is a reinforcement of the lowest-energy dressed mode, which contributes to the energy spectrum of the outgoing beam more strongly than the other modes. This effect is especially pronounced for the one-dimensional box, which indicates that the efficiency of the mode-reinforcement mechanism depends on the steepness of the confinement potential. In this case, a quasi-monochromatic anti-bunched atomic beam is obtained. Results for a bosonic sample are also shown for comparison.Comment: 16 pages, 7 figures, added discussion on time-dependent spectral distribution and corresponding figur