Probing first-order spatial coherence of a Bose-Einstein condensate

Abstract

We probe the spatial coherence properties of a magnetically trapped Bose gas. Two matter wave beams are extracted from two spatially separated regions of the trap and overlap outside the trapping region. The visibility of the resulting interference pattern measures the phase coherence between the regions of extraction. By varying the spatial separation between the two regions the first-order spatial correlation function of the trapped Bose gas can be measured. The location of the minima of the interference pattern is reproducible, which experimentally confirms that the trapped Bose-Einstein condensate is not fragmented into individual condensates.     

Generation of amplitude squeezed states of light from phase squeezed coherent states

Abstract

We propose a scheme to generate a displaced macroscopic superposition of phase squeezed coherent states by incorporating an optical parametric oscillator (OPO) and a nonlinear Kerr medium in a Mach-Zhender interferometer configuration. We show that the phase squeezed coherent state generated by the OPO evolves into a macroscopic superposition of phase squeezed coherent states on spending a specific amount of time inside a Kerr medium. The phase space displacement is achieved by the interference of the intense reference beam with the signal in the final beam splitter of the interferometer. The noise of the reference beam contaminating the signal is prevented by making this beam splitter highly reflective. We have calculated the photon number uncertainty of the outcoming beam and have shown that it is smaller than the usual amplitude squeezed coherent state's value.     

Theory for double beam interference microscopes with coherence effects and verification using the linnik microscope

Abstract

A theoretical model for the interferogram from double beam interference microscopes, which takes into account the coherence effects, is presented. The model is based on the general imaging theory of a lens in defocus. For the case of zero relative lateral displacements between the reference and object beams a simplified expression is found for the defocus and path length dependence of the interferogram. Based on this expression the characteristics of the interferogram are studied and special attention is devoted to explaining the dependence of the fringe size on the objective numerical aperture, and the effect of the spatial and temporal coherence. For the Linnik microscope in which two objectives and a beam splitter cube are used, the effect of the mismatch between chromatic aberrations of the two objectives, and the effect of glass dispersions and misalignment of the beam splitter cube are investigated. Experimental results using the Linnik microscope are presented and they confirm the proposed model.     

Switching and self-trapping dynamics of bose-Einstein solitons

Abstract

We investigate the dynamics of two weakly coupled Bose condensates in long cigar-shaped traps. The Bose condensates are characterized by attractive mean-field interaction and consequently can be studied in terms of bright solitons. We exploit the analogy with directional fibre couplers in nonlinear fibre optics to uncover interesting dynamical regimes like switching of condensates from one trap to another and self-trapping of condensates. We also discuss the analogy between two weakly coupled Bose condensates and the Josephson junction in superfluids and superconductors.     

Study of Induced Temporal Coherence in Optical Parametric Down Conversion

Abstract

Temporal coherence of the idler photon beam induced by a coherent input signal was studied for non-degenerate optical parametric down conversion. When the optical path difference of the interferometer is much longer than the coherence length of the spontaneous idler radiation, the experimental results show that the first-order temporal coherence of the idler photon can be induced by a coherence input signal and the interference fringe visibility is determined by the intensity of the coherent input signal.     

Creation of NOON States from Double Fock-State/Bose-Einstein Condensates

NOON states (states of the form |N〉 _a |0〉 _b +|0〉 _a |N〉 _b where a and b are single particle states) have been used for predicting violations of hidden-variable theories (Greenberger-Horne-Zeilinger violations) and are valuable in metrology for precision measurements of phase at the Heisenberg limit. We show theoretically how the use of two Fock state/Bose-Einstein condensates as sources in a modified Mach Zender interferometer can lead to the creation of the NOON state in which a and b refer to arms of the interferometer and N is the total number of particles in the two condensates. The modification of the interferometer involves making conditional “side” measurements of a few particles near the sources. These measurements put the remaining particles in a superposition of two phase states, which are converted into NOON states by a beam splitter. The result is equivalent to the quantum experiment in which a large molecule passes through two slits. The NOON states are combined in a final beam splitter and show interference. Attempts to detect through which “slit” the condensates passed destroys the interference.     

Interference and the lossless lossy beam splitter

Abstract

By directing the input into a particular mode it is possible to obtain as output all of the input light for a beam splitter which is 50% absorbing. This effect is also responsible for nonlinear quantum interference when two photons are incident on the beam splitter.     

The Schrödinger Cat Family in Attractive Bose Gases

We show that the ground state of an attractive Bose gas in a double well evolves from a coherent state to a Schrödinger Cat like state as the tunneling barrier is decreased. The latter exhibits super-fragmentation similar to the ground state of a spin-1 Bose gas with antiferromagnetic interactions. We also show that the fragmented condensates of attractive and repulsive Bose gases in double wells lead to very different interference patterns.     

Quantum dynamics of the phase of a Bose–Einstein condensate

Abstract

In this review we discuss the dynamics of the phase of trapped Bose–Einstein condensates. In particular we consider the phenomena of phase decoherence (termed also as phase collapse, or diffusion), and phase revival in systems of interacting atoms. We analyse the dependence of the collapse and revival times on the trap potential, dimensionality of the gas, atom number fluctuations, and on the coherent dynamics of the condensate. We show that in a class of experimentally relevant systems, the collapse time is relatively short, and in some cases vanishes in the limit of a large number of atoms, implying that the trapped Bose gas cannot sustain a well-defined quantum phase, and that the phase memory is lost on a relatively short time scale. Furthermore, we calculate the relative atom number fluctuations or a model of two interacting condensates, and show that the fluctuations are generically sub-Poissonian.     

Coherence properties of a continuous atom laser

Abstract

We investigate the coherence properties of an atomic beam evaporatively cooled in a magnetic guide, assuming thermal equilibrium in the quantum degenerate regime. The gas experiences two-dimensional, transverse Bose-Einstein condensation rather than a full three-dimensional condensation because of the very elongated geometry of the magnetic guide. First order and second order correlation functions of the atomic field are used to characterize the coherence properties of the gas along the axis of the guide. The coherence length of the gas is found to be much larger than the thermal de Broglie wavelength in the strongly quantum degenerate regime. Large intensity fluctuations present in the ideal Bose gas model are found to be strongly reduced by repulsive atomic interactions; this conclusion is obtained with a one-dimensional classical field approximation valid when the temperature of the gas is much higher than its chemical potential, k _B T » |μ|.     

Multipass Michelson interferometer with the use of a wavelength-modulated laser diode

An improved multipass Michelson interferometer is implemented. This technique uses the fact that the wavelength of a laser diode varies in proportion to the diode's injection current. With this method the sensitivity augmentation is accomplished by inserting a beam splitter into one arm of the interferometer, resulting in multiple reflections between the end mirror and the beam splitter. In addition, the interference of laser beams reflected from two arms can be accomplished with unequal arms in the condition of a short coherence length. The sensitivity increase of interference fringes and the compensation of the short coherence length have been demonstrated in experiments.     

The dynamics of three-mode coupling in a trapped Bose gas

ABSTRACT

Multiple mode couplings in topological coherent modes of Bose–Einstein condensate are considered, by introducing an external alternating (resonating) field in the system. This analysis is based on the analytical solutions of nonlinear Gross–Pitaevskii equation for a trapped Bose gas at nearly absolute zero temperature. The dynamics of fractional populations of the generated coherent modes are analysed, particularly for a three-level system in the limit of small to large detuning of the intermediate state. These coupled topological modes, though nonlinear, are analogous to a resonant atom and exhibit a variety of significant non-trivial phenomena (effects), like: dynamic phase transitions, interference patterns, critical phenomena, mode-locking and chaotic motion.     

Magnetic Field Dependence of Internal Josephson Effects in Spinor Dipolar Bose–Einstein Condensates

We study internal Josephson effects in spin-1 Bose–Einstein condensates with magnetic dipole–dipole interactions by calculating the Gross–Pitaevskii equations with single mode approximations. The effects represent various oscillating modes given by combinations of 0, π, and running phase modes in Josephson effects in Bose gasses. Especially, we investigate the dependences of a magnetic field on the effects, presenting new dynamics which is not shown elsewhere.     

Coherence Length of a Gaussian-Schell Beam and Atmospheric Turbulence

Abstract

The theoretical relationship between the coherence length and phase-front randomness is analysed using a Gaussian-Schell source and beam model for light propagating through a turbulent atmosphere. Computer results are given which show that partially coherent sources are less influenced by atmospheric turbulence than are coherent sources.     

Dynamics of correlations in atomic Bose-Einstein condensates

Abstract

The Gross-Pitaevskii equation has been extremely successful in the theory of weakly interacting Bose-Einstein condensates. However, present-day experiments reach beyond the regime of its validity due to the significant role of correlations. We review a method for tackling the dynamics of correlations in Bose condensed gases, in terms of non-commutative cumulants. This new approach has a wide applicability in the areas of current interest, e.g. the production of molecules and the manipulation of interactions in condensates. It also offers an interesting perspective on the classical-field methods for partly condensed Bose gases.     

The Birth of a Phase-cat

Abstract

We present a recipe for constructing a phase-cat, that is a superposition of two coherent states of identical phase but different amplitudes. The method relies on an effective rotation of an amplitude-cat, that is a superposition of two coherent states with identical amplitudes but different phases. We create the amplitude-cat by a dispersive atom-field interaction and achieve its effective rotation via the combination of two beam splitters and a phase shifter. We optimize the amount of phase narrowing by choosing the appropriate initial atomic superposition and by performing the appropriate delayed measurement of the final atomic coherence.     

Method for Birefringence Measurements with Correction of Errors Due to Multiple Reflection in Anisotropic Plates

Abstract

Birefringence measurements of anisotropic plates using coherent light are affected by errors due to the multiple reflections in the investigated plate. An evaluation method for measuring birefringence is presented, where the intensity distributions of two light beams are used for the correction of these errors. These beams arise from a polarizing beam splitter, which is the analyser of the polarization system. In this paper, a theoretical treatment is given which shows that this method results in more accurate values than the usual methods, especially for highly refractive materials with a small birefringence.     

Quantum Noise Reduction by Photodetection with Feedback

Abstract

A simple model is proposed to account for the generation of sub-shot noise light by feedback of the photocurrent. The model is based on a variable beam splitter controlled by the photocurrent from a detector placed after the beam splitter. The zero-feedback transmittivity is not necessarily unity. The field transmitted by the beam splitter shows reduced photon noise when the feedback causes a decreasing transmittivity.     

Diffractive shaping of excimer laser beams

Abstract

We address the problem of shaping the intensity distribution of a highly directional partially coherent field, such as an excimer laser beam, by means of diffractive optics. Our theoretical analysis is based on modelling the multi-transverse-mode laser beam as a Gaussian Schell-model beam. It is shown numerically that a periodic element, which is unsuitable for the shaping of a coherent laser beam, works well with an excimer laser beam because of its partial spatial coherence. The conversion of an approximately Gaussian excimer laser beam into a flat-top beam in the Fourier plane of a lens is demonstrated with a diffractive beam shaper fabricated as a multilevel profile in SiOl by electron-beam lithography and proportional reactive-ion etching.     

Generation of partially coherent laser beam directly from spatial-temporal phase modulated optical resonators

Abstract

The generation of a partially coherent laser beam directly from a spatial-temporal phase modulated optical resonator is investigated both experimentally and theoretically. The laser material used in the experiment is Nd:YAG rod pumped by Krypton lamps working in continuous wave mode. The phase modulation is fulfilled by an intra-cavity LiNbO₃ electro-optic crystal driven by high voltage. The experimental results show that intracavity phase modulation is an effective way to generate partially coherent laser beams. The theoretical analysis and numerical simulation shows that the output beam can be characterized by Gaussian Schell-model (GSM) beams. The two-slit interference experiment confirms that the output beam is partially coherent.