Effect of a Squeezed Vacuum on Coherent Population Trapping in a Three-level Lambda System

Abstract

Master equation methods are used to investigate the effects of a broad-band squeezed vacuum on a three-level atom of the lambda configuration. The two-mode squeezed vacuum is treated as a Markovian reservoir in a non-stationary phase-dependent state. In addition to the squeezed vacuum the atom is driven by two coherent laser fields each of which, depending on the polarization, can couple to one or both of the atomic transitions. We show that in general the optical Bloch equations for the atomic density matrix elements have oscillatory coefficients, thereby necessitating the use of Floquet methods. For the case of equal laser frequencies, which are also equal to the carrier frequency of the squeezed vacuum, the coefficients of the Bloch equations become time independent and stationary solutions for the populations and coherences are obtained by standard matrix methods. For the ordinary vacuum the usual coherent population trapping effect at two-photon resonance is obtained, with the upper state population being zero. An unsqueezed thermal field partially destroys the trapping effect as the upper state population is no longer zero at two-photon resonance. The squeezed vacuum has the effect of improving the trapping in that the coherence hole becomes more pronounced for some values of the relative phase between the squeezed vacuum and the driving fields. The additional effects of a coherence transfer rate between the two optical coherences, which occurs for special choices of angular momentum quantum numbers are also studied. For the case of equal laser frequencies, the inclusion of this coherence transfer process destroys population trapping and reduces the lambda system to a two-level system. However, for the case of unequal laser frequencies, the coherence transfer process in combination with the squeezed vacuum can restore to some extent the population trapping. We show that other features that do not occur for two-level atoms, such as stationary population inversions between pairs of the atomic levels, also depend on the relative phase and can be enhanced in the squeezed vacuum. In the case of unequal frequencies of the driving fields the population in the upper state depends on the relative phase only when the carrier frequency of the squeezed vacuum is equal to one of the two frequencies of the driving fields. When the carrier frequency of the squeezed vacuum is slightly detuned from both frequencies of the driving fields, the population in the upper state is insensitive to the relative phase but is dependent on the degree of squeezing. For large detunings, the population does not show any dependence on the degree of squeezing and its distribution in function of the two-photon detuning is similar to that in the thermal vacuum field.     

Permanently disentangled states of atom–field system via spontaneously generated coherence

Abstract

The effect of spontaneously generated coherence on evolution of the entanglement between a driven four-level Y-type atom and its spontaneous emission field is studied. We have shown that the atom will be entangled to its spontaneous emission field due to spontaneously generated coherence and coherent population trapping at the steady state. It is found that the degree of entanglement strongly depends on the initial atomic state. So, it can be controlled by the pumping laser pulses used for preparing an initial atomic system. More interestingly, the atom–field system can be found in a permanently disentangled state for a properly prepared atom.     

Coherence phenomena in coupled pptical resonators

Abstract

We predict a variety of photonic coherence phenomena in passive and active coupled ring resonators. Specifically, the effective dispersive and absorptive steady-state response of coupled resonators is derived, and used to determine the conditions for coupled-resonator-induced transparency and absorption, lasing without gain, and cooperative cavity emission. These effects rely on coherent photon trapping, in direct analogy with coherent population trapping phenomena in atomic systems. We also demonstrate that the coupled-mode equations are formally identical to the two-level atom Schrödinger equation in the rotating-wave approximation, and use this result for the analysis of coupled-resonator photon dynamics. Notably, because these effects are predicted directly from coupled-mode theory, they are not unique to atoms, but rather are fundamental to systems of coherently coupled resonators.     

Effects of Atomic Coherence on Collapses and Revivals in the Binomial State of the Field

Abstract

The effects of the coherence between the states of a two-level atom on the phenomenon of collapses and revivals in an undamped binomial state of the electromagnetic field are investigated. It is found that the Rabi oscillations exhibit qualitatively different behaviour for different phases of coherence between the levels. This behaviour in the binomial state of the field is in contrast with that in a coherent state field, in which case the Rabi oscillations are qualitatively the same for all values of the coherence between the two atomic levels.     

Field oscillations in a micromaser with injected atomic coherence

Abstract

The electric field in a lossless, regularly-pumped micromaser with injected atomic coherence can undergo a period-two oscillation in the steady state. The field changes its value after a single atom passes through the micromaser cavity, but returns to its original value after a second atom travels through. We give a simple explanation for this phenomenon in terms of tangent and cotangent states. We also examine the effect of cavity damping on this steady state.     

Coherence of bose condensates

Abstract

We study the coherence of interacting Bose condensates in recent magnetic trap experiments. The coherent evolution manifests itself in the macroscopic interference of two independent Bose condensates. The theoretical predictions from the time-dependent Gross–Pitaevskii equation are in excellent agreement with the measured interference patterns. A coherent coupling of two condensates represents the atomic analogon of a Josephson junction. The dependence of the magnetic confinement on the nuclear spin orientation allows one to build a controllable beam splitter by magnetic resonance. The application of this beam splitter to realize an atom laser is studied theoretically. The coherence of the output beam is limited only by phase diffusion of the condensate.     

A variable lateral-shearing Sagnac interferometer with high numerical aperture for measuring the complex spatial coherence function of light

Abstract

We combine a telescopic imaging system with a common-path, lateral-shearing interferometer and use phase-shifting interferometry to measure the complex spatial coherence function (or mutual intensity) of a linearly-polarized optical field. Our telescopic design increases the numerical aperture of the system without distorting the shape of the wave front, and therefore without changing the phase difference between lateral positions in the optical field. Our method of generating lateral-sheared images introduces no additional astigmatism. To demonstrate the use of the interferometer we extract the information contained in the complex spatial coherence function to reconstruct the amplitude and phase of a coherent optical field, and we also show how the spatial coherence function evolves from a coherent field to a partially coherent one as light traverses a random multiple-scattering medium.     

Collapse-revival Phenomenon in the Jaynes-Cummings Model Interacting with the Multiphoton Holstein-Primakoff SU(2) Coherent State

Abstract

We have analysed the behaviour of the atomic population inversion of the two-level atom interacting with a single-mode field initially prepared in the multiphoton Holstein-Primakoff SU(2) coherent state. It is shown that the behaviour of the atomic inversion depends on the parameters characterizing the initial state of the field. In particular, the atomic inversion can exhibit periodical oscillations as well as the collapse-revival phenomenon.     

Adiabatic transfer between cavity modes

Abstract

The idea of counter-intuitive transfer is taken over from atomic systems to a two-mode Jaynes-Cummings model with degenerate mode frequencies. We show that an arbitrary photon state can be transferred between the two modes utilizing a suitable pulse sequence. The method is illustrated by the transfer of pure n-states and coherent states. The numerical analysis of the situation allows us to determine which parameters give adiabatic transfer and the magnitude and character of the corrections. The method is related to earlier work and possible extensions are discussed.     

Quantum dynamical properties of a two-photon non linear Jaynes-cummings model

Abstract

In this paper a two-photon Jaynes-Cummings model interacting with a Kerr-like medium is studied. It is assumed that the electromagnetic field is in different states such as coherent, squeezed vacuum and pair coherent, and that the atom is initially in the excited state. The temporal evolution of the population of the excited level, and the second-order coherence function are studied. The results obtained show that this system has some similarities with the two-mode Stark system. Two photon entanglement are analysed at different initial conditions.     

N-level Atom Interacting with Single-mode Radiation Field: An Exactly Solvable Model with Multiphoton Transitions and Intensity-dependent Coupling

Abstract

We study the dynamics of an N-level atom coupled in a lossless cavity to a single-mode near-resonant quantized field. The atomic levels are coupled by the multiphoton transitions and the coupling constants between the field and the atomic levels are supposed to be intensity dependent. We find the exact solution for the state vector describing the dynamics of the atom-plus-field system. As an illustration we use the model for studying (i) the time evolution of the atomic occupation probability with the initially coherent field and (ii) the light squeezing, when the cavity field is initially in the vacuum state and the atom is prepared in the atomic ‘coherent state’ (a superposition of atomic states).     

Comment: There is no unmet requirement of optical coherence for continuous-variable quantum teleportation

Abstract

It has been argued that continuous-variable quantum teleportation at optical frequencies has not been achieved because the source used (a laser) was not ‘truly coherent’. Here it is shown that ‘true coherence’ is always illusory, as the concept of absolute time on a scale beyond direct human experience is meaningless. A laser is as good a clock as any other, even in principle, and this objection to teleportation experiments is baseless.     

Quantum coherence effects in a Raman amplifier

We have studied optical pulse propagation in a Raman fiber amplifier doped with a three-level medium and driven by a control laser pulse. We analyze the spatial-temporal dynamics of pulse propagation for different atomic initial conditions. The propagation of an optical pulse through the amplifier can be sustained by a control laser that induces transparency via quantum coherence, which is useful for extending the distance between optical repeaters. Under certain conditions, amplification is achieved without population inversion. The results could be useful for laser control of optical pulses in amplifiers and waveguides.     

Axial intensity distribution of partially coherent light focused by a lens with spherical aberration

Abstract

The focusing of partially coherent light by a lens with spherical aberration (SA) is studied. The numerical calculation results are given, showing that the axial intensity distribution not only depends on the SA, but also on the coherence of partially coherent light and the Fresnel number of the lens. As the coherence decreases, the influence of the SA on the axial intensity distribution decreases, and the positions of maximum axial intensity shift towards the lens.     

Transformation of coherence and of the spectrum of light by a moving diffuser

Abstract

Effects of a diffuser on the spectral degree of coherence and on the spectrum of light produced by transmitting light through the diffuser are described. Both stationary and uniformly moving diffusers are considered and the analysis applies to dielectric as well as to absorbing diffusers. The results are illustrated by numerical examples.     

Controlling decoherence of a two-level atom in a lossy cavity

Abstract

By use of external periodic driving sources, we demonstrate the possibility of controlling the coherent as well as the decoherent dynamics of a two-level atom placed in a lossy cavity. The control of the coherent dynamics is elucidated for the phenomenon of coherent destruction of tunnelling (CDT), i.e. the coherent dynamics of a driven two-level atom in a quantum superposition state can be brought practically to a complete standstill. We study this phenomenon for different initial preparations of the two-level atom. We then proceed to investigate the decoherence originating from the interaction of the two-level atom with a lossy cavity mode. The loss mechanism is described in terms of a microscopic model that couples the cavity mode to a bath of harmonic field modes. A suitably tuned external cw-laser field applied to the two-level atom slows down considerably the decoherence of the atom. We demonstrate the suppression of decoherence for two opposite initial preparations of the atomic state: a quantum superposition state as well as the ground state. These findings can be used to decrease the influence of decoherence in qubit manipulation processes.     

Entanglement induced by spontaneous emission in spatially extended two-atom systems

Abstract

The role of the collective antisymmetric state in entanglement creation by spontaneous emission in a system of two non-overlapping two-level atoms has been investigated. Populations of the collective atomic states and the Wootters entanglement measure (concurrence) for two sets of initial atomic conditions are calculated and illustrated graphically. Calculations include the dipole-dipole interaction and a spatial separation between the atoms that the antisymmetric state of the system is included throughout even for small interatomic separations. It is shown that spontaneous emission can lead to a transient entanglement between the atoms even if the atoms were prepared initially in an unentangled state. It is found that the ability of spontaneous emission to create transient entanglement relies on the absence of population in the collective symmetric state of the system. For the initial state of only one atom excited, entanglement builds up rapidly in time and reaches a maximum for parameter values corresponding roughly to zero population in the symmetric state. On the other hand, for the initial condition of both atoms excited, the atoms remain unentangled until the symmetric state is depopulated. A simple physical interpretation of these results is given in terms of the diagonal states of the density matrix of the system. We also study entanglement creation in a system of two non-identical atoms of different transition frequencies. It is found that the entanglement between the atoms can be enhanced compared to that for identical atoms, and can decay with two different time scales resulting from the coherent transfer of the population from the symmetric to the antisymmetric state. In addition, it was found that a decaying initial entanglement between the atoms can display a revival behaviour.     

Entropy Evolution of the Bimodal Field Interacting with an Effective Two-level Atom Via the Raman Transition

Abstract

The properties of entropy evolution of the bimodal field interacting with an effective two-level atom via the Raman transition are studied. The influences of the initial average photon number and of the atomic coherence on the evolution of the bimodal field entropy are examined. It is shown that the bimodal field is in a pure state only under certain conditions in the early stages of time evolution and later tends to a statistical mixture state with maximum entropy values; the bimodal field remains strongly entangled with the atom.     

Generating squeezed states by strong laser-atom interaction

Abstract

A proof is given using, a quantized single mode field in interaction with an atom in non-relativistic approximation, that the scattered light in strong laser–atom interaction can be made coherent to squeezed by properly choosing the wavelength of the laser, the density of the sample of atoms at the laser beam and the pulse duration. In the experiments with gases for harmonic generation, at the current laser wavelengths this effect is too small to be observed and the term of the square of the field in the Hamiltonian can be safely neglected. Then, the observed light is purely coherent.     

Photosynthetic light harvesting: excitons and coherence

Photosynthesis begins with light harvesting, where specialized pigment–protein complexes transform sunlight into electronic excitations delivered to reaction centres to initiate charge separation. There is evidence that quantum coherence between electronic excited states plays a role in energy transfer. In this review, we discuss how quantum coherence manifests in photosynthetic light harvesting and its implications. We begin by examining the concept of an exciton, an excited electronic state delocalized over several spatially separated molecules, which is the most widely available signature of quantum coherence in light harvesting. We then discuss recent results concerning the possibility that quantum coherence between electronically excited states of donors and acceptors may give rise to a quantum coherent evolution of excitations, modifying the traditional incoherent picture of energy transfer. Key to this (partially) coherent energy transfer appears to be the structure of the environment, in particular the participation of non-equilibrium vibrational modes. We discuss the open questions and controversies regarding quantum coherent energy transfer and how these can be addressed using new experimental techniques.