Table of contents

Volume 4

Number 1, February 2002

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EDITORIAL

001

Guest editors: A Hemmerich, W Vassen and E Arimondo

Topics to be covered include:

  • Bose-Einstein condensation

  • Fermi degenerate gases

  • Characterization and manipulation of quantum gases

  • Coherent and nonlinear cold matter wave optics

  • New schemes for laser cooling

  • Coherent cold molecular gases

  • Cold atoms and ultra-precise atomic clocks

  • Applications of cold quantum gases to metrology and spectroscopy

  • Applications of cold quantum gases to quantum computing

  • Nanoprobes and nanolithography

This topical issue is in connection with `Lunteren2002' the 7th International Workshop of Atom Optics and Interferometry, Lunteren, The Netherlands, 28 September-2 October 2002.

The topical issue is scheduled for publication in April 2003. All papers will be refereed according to the high standards of the journal and authors will receive 25 free offprints of their published paper and a complimentary copy of the topical issue. There are no page charges for publication. Manuscripts should be prepared following the general guidelines for authors published in the journal. Full instructions can be found in our Notes for authors. Please include a covering letter stating that the submission is intended for the Cold quantum gases special issue, to avoid treatment as a regular submission.

Manuscripts should be submitted to the Publisher by 1 October 2002, although authors are strongly encouraged to submit their work as soon as possible.

LETTER TO THE EDITOR

L1

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The dynamics of power distribution between longitudinal modes of a multimode semiconductor laser subjected to external optical feedback is experimentally analysed in the low-frequency fluctuation regime. Power dropouts in the total light intensity are invariably accompanied by sudden activations of several longitudinal modes. These activations are seen not to be simultaneous to the dropouts, but to occur after them. The phenomenon is statistically analysed in a systematic way, and the corresponding delay is estimated.

REVIEW ARTICLE

R1

Seventy five years ago, three remarkable papers by Schrödinger, Kennard and Darwin were published. They were devoted to the evolution of Gaussian wave packets for an oscillator, a free particle and a particle moving in uniform constant electric and magnetic fields. From the contemporary point of view, these packets can be considered as prototypes of the coherent and squeezed states, which are, in a sense, the cornerstones of modern quantum optics. Moreover, these states are frequently used in many other areas, from solid state physics to cosmology. This paper gives a review of studies performed in the field of so-called `nonclassical states' (squeezed states are their simplest representatives) over the past seventy five years, both in quantum optics and in other branches of quantum physics.

My starting point is to elucidate who introduced different concepts, notions and terms, when, and what were the initial motivations of the authors. Many new references have been found which enlarge the `standard citation package' used by some authors, recovering many undeservedly forgotten (or unnoticed) papers and names. Since it is practically impossible to cite several thousand publications, I have tried to include mainly references to papers introducing new types of quantum states and studying their properties, omitting many publications devoted to applications and to the methods of generation and experimental schemes, which can be found in other well known reviews. I also mainly concentrate on the initial period, which terminated approximately at the border between the end of the 1980s and the beginning of the 1990s, when several fundamental experiments on the generation of squeezed states were performed and the first conferences devoted to squeezed and `nonclassical' states commenced. The 1990s are described in a more `squeezed' manner: I have confined myself to references to papers where some new concepts have been introduced, and to the most recent reviews or papers with extensive bibliographical lists.

PAPERS

1

The structure of the quantum-mechanical inhomogeneous symplectic group ISp(2,C) in single boson mode is discussed and, in addition to its most common realization by quadratic combinations of the boson annihilation and creation operators, other nonlinear realizations are considered. The most basic disentanglement relations of the separation of squeezing (including rotation) and displacement operators are derived using a three-dimensional fundamental representation. The phase factors are determined using a special approach involving transformation of the inhomogeneous quadratic form in the boson operators to a central point together with special normal- and antinormal-ordering relations. In appendix B, the most basic formulae of operator disentanglement are collected together and special cases of the derived relations are considered.

15

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We perform a theoretical analysis of steady-state solutions and quantum noise in a below-threshold optical parametric oscillator (OPO) operating as an amplifier with an input seed wave. Both the amplitude-squeezed and phase-squeezed states of the output field are considered. We take into account the intracavity nonlinear losses due to intracavity frequency doubling of the signal wave and the quantum fluctuations of the seed and pump waves. Unlike the preceding theoretical studies of the problem, we show that squeezing in bright beams produced by the OPO depends on their intensity. For the amplitude-squeezed state, squeezing strongly degrades with increasing output intensity. In contrast, one can obtain good squeezing for phase-squeezed beams of high output intensity.

20

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Experiments showing period three intensity oscillations are reported for a semiconductor laser subject to external injection. These oscillations appear close to a period doubling bifurcation of the fundamental laser limit-cycle. We show numerically that they correspond to an isolated branch of solutions of the laser rate equations. We also show that the sequence of numerical spectra for the period one, period two and period three limit-cycle regimes compare well with the experimental spectra obtained by progressively increasing the injection rate. Finally, we investigate the period three branch of solutions by using a numerical continuation method that follows both stable and unstable solutions.

27

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We analyse the two longitudinal mode threshold of a solid-state Fabry-Perot laser with a spatially nonuniform pump for two configurations: an end-pumped laser and a laser with a partially filled cavity. The threshold is derived in a consistent way. We prove that inhomogeneous pumping or partial filling of the cavity hardly modify the two-mode threshold.

30

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The interaction between an ultracold cascade three-level atom and a two-mode cavity field has been studied. The effects of the centre-of-mass motion, the cavity length, the coupling constants, the initial field states and the initial field intensity on the atomic dynamics have been examined. We have found that the population probabilities show dependence on the interaction time in the fast-atom region while they show dependence on the interaction length in the slow-atom region. The variations of the probabilities versus the cavity length show resonant peaks, and the peaks become sharper as the atom moves more slowly. The coupling constants, the initial field states and the initial field intensity also influence the atomic dynamics significantly. The two transitions are competitive for the atomic probability in the middle state, while they are cooperative for that in the lower state.

37

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We extend our earlier investigations (Furuichi S and Abdel-Aty M 2001 J. Phys. A: Math. Gen.34 6851) on the entanglement degree of a two-level atom to include any forms of nonlinearities of both the field and the intensity-dependent atom-field coupling. We present a derivation of the unitary operator within the frame of the dressed state approach, by means of which we identify and numerically demonstrate the region of parameters where significantly large entanglement can be obtained. The influences of the nonlinearity, Stark shifts and detuning on the degree of entanglement are examined. It is shown that features of the degree of entanglement are influenced significantly by the kinds of nonlinearity of the single-mode field. The model presented in this paper can be regarded as a generalization of the Jaynes-Cummings model.

44

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Recently we introduced an extremely simple device for measuring ultrashort laser pulses, which utilizes a thick nonlinear-optical crystal, that replaces the usual thin nonlinear-optical medium and spectrometer simultaneously. It also replaces the usual beamsplitter and delay line with a single optic, a Fresnel biprism, which requires no alignment. Here we review the operation of the device and show that dithering the lateral position of the input beam in such a device increases the spectral range of the device with no loss in spectral resolution. Furthermore, we show that it separates the two constraints on crystal selection, allowing the measurement of a wider range of spectrally broader and/or more complicated pulses.

49

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In the present study we extend and generalize previous results for coherent-state and squeezed-state Michelson interferometer quantum mechanical uncertainties (or fluctuations), which are commonly referred to as `quantum noise'. The calculation of photon counting (PC) fluctuations in the squeezed-state interferometer is extended to fourth-order correlation functions used as the measured signal. We also generalize a `unified model' for treating both PC and radiation pressure fluctuations in the coherent-state interferometer, by using mathematical methods which apply to Kerr-type interactions. The results are more general than those reported previously in two ways. First, we obtain exact expressions, which lead to previous results under certain approximations. Second, we deal with cases in which the responses of the two mirrors to radiation pressure are not equal.

57

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In this paper, we present the first data from a new double MOT Bose-Einstein condensation (BEC) experiment. To assist new groups in their pursuit of BEC, we present a typical series of absorption images over an evaporative cooling ramp when BEC is reached, and compare this with a second series where the machine fails to reach condensation. All pictures in both series are presented on the same scale allowing the trend in the elastic collision rate as evaporation proceeds to be assessed simply by looking at the pictures. This is a powerful and simple diagnostic that is easily applied in the laboratory when characterizing and trouble shooting a new machine.

62

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We analyse the time-of-flight method of measuring the temperature of cold trapped atoms in the specific case of short distances of the probe beam from the trap centre and finite atomic cloud size. We theoretically examine the influence of the probe beam shape and its distance from the initial position of the cloud on the temperature evaluation. These results are then verified with a three-dimensional Monte Carlo simulation and applied to our experimental data to show that the proposed procedure allows accurate and reliable determination of the temperature.

67

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Laser spectra are strongly modified by the optical feedback which is provided by external cavities; here we give a preliminary experimental result describing the optical spectrum of a fibre laser having two identical end cavities, which appear between the external mirrors and fibre ends. One observes a channelled spectrum including mode clusters separated by empty regions. We use the optical Airy function defined in the pure frequency domain to study these spectra. An optical Vernier effect allows the description of this structure. The linewidth of each mode is calculated as a function of the gain, by using the same Airy function.

75

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We have demonstrated that coherent control of the momentum exchange between a light field and atoms can be implemented in frequency-modulated light. The optical parameters are chosen to drive the atoms between ground and excited states by adiabatic rapid passage in counterpropagating modulated light beams. We apply the optical force transversely to a thermal atomic beam, and the deflection provides a measure of the force. The modulation period is 2π/ωs<<τ, and each half-cycle exchanges momentum 2ℏk, so the resulting force is much greater than the ordinary radiative force. Moreover, the velocity range of the force in such a light field is much greater than that of the radiative force. This constitutes another example of the huge range of capabilities of optical forces in non-monochromatic light.

80

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Novel states called trio coherent states are introduced and studied. It is shown that these states possess inherent nonclassical properties such as sub-Poissonian number distributions and violation of Cauchy-Schwarz inequalities. Concerning squeezing, though the usual multimode squeezing is absent, a new type of higher-order multimode squeezing may occur in a trio coherent state. Finally, an experimental scheme is proposed to generate the introduced trio coherent state.