Interaction of Superpositions of Coherent States of Light with Two-level Atoms

Abstract

We investigate some of the basic features of the interaction of superpositions of coherent states of light with two-level atoms in the framework of the Jaynes-Cummings model. We compare the behaviour of the system in the case of having a coherent superposition state and a statistical mixture of coherent states as an initial field. We investigate the collapses and revivals of the atomic inversion by studying the evolution of the Q function of the cavity field. We also establish the connection between the purity of the field and the collapses and revivals of the atomic inversion.     

Interaction of Squeezed Light with Two-level Atoms

Abstract

We investigate some of the fundamental features of the interaction of squeezed light with two-level atoms in the framework of the Jaynes-Cummings model. We start our analysis by calculating the collapses and revivals of the atomic inversion. We discuss the degree of purity of the field (given by the entropy) and its disentanglement from the atomic source. The connection with the evolution of the Q-function is also made. We notice that contrary to the coherent state case, the field turns into a nearly pure (squeezed) state at the revival time as if the field was prepared in a coherent state. The field also becomes a superposition of squeezed states at half of the revival time, and this is confirmed by investigating the photon number distribution. The phase properties of the field are discussed using the Pegg-Barnett formalism.     

Quantum Superpositions of Binomial States of Light

We introduce new kinds of states of electromagnetic field, which are quantum superpositions of binomial states. They not only exhibit remarkable non-classical properties but can also interpolate between the ‘Schrödinger cat’ type of states and the number states in a particularly interesting way. We basically discuss some of their main statistical properties, as well as schemes for their generation. We also employ quasiprobability distributions in phase space.     

Interaction of a Two-level Atom with Squeezed Light

The dynamic response of the inversion in a two-level atom to single-mode squeezed states of the radiation field is examined. Depending on the direction of squeezing, an increase or decrease in the collapse time is demonstrated. A number of additional departures from the response of the atom to a coherent field are noted. In particular, for certain squeezed states the response of the atom is similar to that expected for chaotic radiation.     

Sub-radiant States of a Spatially Extended System of N Two-level Atoms

Abstract

The existence of sub-radiance is demonstrated for a generalized rotating-wave approximation Dicke Hamiltonian model characterized by an arbitrary space dependence of the coupling constants of N two-level atoms to a single mode of a radiation field. To deduce this result we first establish the form of a characteristic equation for sub-radiance and then solve it by introducing a suitable non-unitary operator. In this way the explicit form of all the sub-radiant states of the spatially extended model are easily obtained from those that are well known and relative to the point-like Dicke model. Our investigation clearly shows that inhomogeneous coupling of the N atoms with the field is compatible with sub-radiant behaviour.     

The Interaction of Displaced Number State and Squeezed Number State Fields with Two-level Atoms

Abstract

The time-evolution of a single two-level atom in a single-mode high-Q cavity is sensitive to the quantum fluctuations of the cavity radiation field and to its photon statistics: this sensitivity is realizable experimentally in the Rydberg atom micromaser. We study the effects of the interaction of a two-level atom with two new non-classical radiation fields: the squeezed number state and the displaced number state realizable by nonlinear and linear transformations of field number states which have an initially precise occupation number. The time-varying field fluctuations caused by the atomic interaction are described using the Q-function quasi-probability.     

Interaction of a System of Initially Unexcited Two-level Atoms with a Weak Cavity Field

Abstract

Using a perturbation method, constructed in terms of SU(2) group representations, the interaction of N initially unexcited two-level atoms and a weak single-mode cavity field is studied. The field is assumed to be initially either in a Fock state with a number of photons equal to n or in a coherent state. In the case of the photon-number state with n  3, the pure phenomenon of collective collapses and revivals manifests itself. For the initially coherent field the phenomenon of collapses and revivals arising from the photon number distribution mechanism is additionally modulated by this collective mechanism. The problem of the interaction of excited atoms with an initially coherent field has already been solved numerically by Barnett and Knight. For n=1 2 and 3 the approximate solution is compared with the exact solutions also given in this paper and the limit of applicability of our approach is established.     

Multimode Coherent States and HeNe Laser Light

Abstract

Among the quantum optical states of a tremolant optical cavity are multimode coherent states. Such states are also possible in open cavities where the cavity stabilization time is greater than the multimode beat time. In open cavity resonator lasers they reduce the power limiting effects of spectral hole burning and therefore tend to grow at the expense of single mode coherent states.     

Squeezing in Finite Superpositions of Photon-number States without the Vacuum

Abstract

We show that a finite superposition of photon-number states without the vacuum state can lead to squeezed fluctuations. The properties of these states are discussed.     

Berry's Phase in the Coherent Excitation of Atoms

Abstract

The adiabatic variation of a Hamiltonian can cause the wavefunction, governed by the Hamiltonian, to acquire an unexpected phase. The existence of this phase (Berry's phase) is an additional element in the well-known quantum adiabatic theorem. Berry's phase is observable in the interference between two identically prepared systems only one of which is adiabatically varied. We show that a single quantum system prepared in a superposition of the eigenstates of its Hamiltonian leads to observable Berry phase effects at all times. We examine this principle within the context of two-level optical resonance.     

Information Processing with Coherent Light

In any plane of an optical tract coherent light is fully described by the complex amplitude, that is to say by a two-valued function. Nevertheless, it can be also described by a one-valued or real function, such as photographic density plus a known, coherent reference wave. This is the basis of wavefront reconstruction or holography. The history of holography is presented, and some of its applications, such as holographic interferometry, contour mapping and three-dimensional pictures in monochrome or in natural colours are discussed. Some prospective applications are holographic panoramas and three-dimensional projection of moving pictures. Information coding and storage are very promising applications, but held up by the phenomenon of ‘laser speckle’. Finally it is pointed out that holographic coding, which is a very complicated and multi-dimensional type of coding, has greater potentiality than expected on the basis of Shannon's communication theory. With a code of blocks consisting of N data only N data can be transmitted exactly, but a much greater number can be transmitted with a tolerable error. J. P. Wild's Culgoora radioheliograph, which maps 3000 points with only 96 aerials by a method which could be (though for economy reasons is not) simultaneous, can be considered as the first practical application of this principle.     

Generation and Properties of Superpositions of Displaced Fock States

Abstract

We study the statistical properties of superpositions of displaced Fock states. We find that for the superposition of the form ¦ψ₁〉 = 1/√2(¦α, n〉 + ¦α, k〉) the direction of the displacement (α positive or negative) plays an important role; also, if n = 1 and k = 0 a strong sub-Poissonian character is found for α ≥ 0. We also analyse the ways in which superpositions of displaced Fock states may be generated.     

Collapse-revival Phenomenon in the Process of k-photon Down Conversion with Superpositions of Number States

Abstract

We calculate numerically the time evolution of the mean photon number in the process of k-photon down conversion process with quantized pump. The pump mode was supposed to be initially in a superposition of number states and the down converted mode in a number state. We analysed in some detail the influence of the initial field statistics of the pump mode as well as the presence of non-vacuum number states in the down converted mode on the appearance of collapses and revivals.     

Rate-equation and Bloch-equation Theories of Radiation Pressure on Two-level Atoms

Theories of radiation pressure based on rate equations and on the optical Bloch equations are developed within a common framework that allows comparison of the two. The latter method is used to determine the time dependence of the mean momentum of a two-level atom subjected to monochromatic coherent light for general values of various broadening parameters and detuning. The expression for the corresponding radiation pressure force in the limit of steady-state atomic level populations includes previous results as special cases. The rate equation method provides a fully quantum-mechanical calculation of an expression obtained by Einstein for the rate of change of mean-square atomic momentum in thermal equilibrium.     

Radiance Theorem with Partially Coherent Light

The transmission of a generalized radiance across a planar boundary separating two homogeneous media is considered. It is assumed that the optical field remains continuous at the interface and reflection is neglected. A result is obtained which may be regarded as a generalization of the conventional radiance theorem for fields of any state of coherence. This result differs from the conventional theorem by a factor that depends, in general, both on the optical intensity and on the degree of coherence of the field. However, over a wide range of circumstances the generalized radiance theorem is shown to be in good agreement with the conventional theorem.     

Entangled Coherent States with Variable Weighting

Abstract

Entangled coherent states, with arbitrary weighting of the two product coherent states in the superposition, might be produced by incorporating an optical bistable device in a coupled cavity configuration. This scheme is contrasted with the entangled coherent states that arise due to interaction in an optical Kerr medium and produce only equally weighted entanglements. The entanglement is shown to occur, not between coherent states, but between states which closely approximate coherent states. An interaction which does produce entanglement between true coherent states is introduced but is shown to be unphysical.     

On the Squeezing of Coherent States by the Multiphoton Jaynes-Cummings Hamiltonian with an Intensity-dependent Coupling

Abstract

The squeezing properties of the multiphoton Hamiltonian with intensity-dependent coupling are evaluated for the [xcirc] and [pcirc] _x quadratures, for the initial state of a coherent electromagnetic field and an atom in the ground state. Two measures of squeezing: the percentage of total squeezing and the squeezing time-period percentage, are introduced. Interesting squeezing properties with respect to [xcirc] are observed for real coherent states when the time evolution of the above measures and of the time-averaged squeezing are analysed. The multiphoton intensity-dependent coupling Hamiltonian is found to be almost independent of the specific powers of the annihilation and creation operators, as long as the sum of the powers is kept constant.     

Optical Imaging with Partially Coherent Non-thermal Light

The reconstruction of an object from its image is studied from the point of view of the coherence theory including detection in the process of imaging. Finite-size objects permit the use of the theory of entire functions to prove that if the transformation from object to image is linear (detection is not included in imaging) the object can be reconstructed uniquely. Non-linear transformations from object to image (detection is included in imaging) for weak visibility objects and for a particular choice of the diffraction function are also studied. In the first case a finite-size object is determined uniquely, in the second case the reconstructed object is determined apart from the phase, which can sometimes be determined from the dispersion relations. Further, the similarity between an object and its image is investigated. It is shown that partial coherence creates typical non-linearity in imaging which results in an interval of eigenvalues (similarity coefficients) and that there may arise the branching of a structure imaged similarly into several structures imaged similarly.     

Bunching and Antibunching Effects in a System of N Two-level Atoms

Abstract

The problem of exhibiting bunching and antibunching phenomena for a system of N two-level atoms in interaction with light is investigated. The conditions for the change from bunching to antibunching and vice versa are obtained for resonance, and for time-independent and time-dependent coupling constant. The conditions for the case of resonance and time-independent coupling constant are investigated for both generalized coherent states and squeezed coherent states.     

Interaction of Helium Rydberg State Atoms with Superfluid Helium

The pair potentials between ground state helium and Rydberg He $^*(2s,2p,3s)$ atoms are calculated by the full configuration interaction electronic structure method for both the electronic singlet and the triplet manifolds. The obtained pair potentials are validated against existing experimental molecular and atomic data. Most states show remarkable energy barriers at long distances ( $R > 5$ Å), which can effectively stabilize He $^*$ against the formation of He $_2^*$ at low nuclear kinetic energies. Bosonic density functional theory calculations, based on the calculated pair potential data, indicate that the triplet ground state He $^*$ reside in spherical bubbles in superfluid helium with a barycenter radius of 6.1 Å at the liquid saturated vapor pressure. The pressure dependency of the relative He $^*$ $2s$ $^3S$ $\rightarrow $ $2p$ $^3P$ absorption line blue shift in the liquid was obtained through both the statistical line broadening theory as well as the dynamic adiabatic following method. The pronounced difference between the results from the static and dynamic models is attributed to the dynamic Jahn–Teller effect that takes places in the electronically excited state within the dephasing time of 150 fs. Transient non-thermalized liquid surroundings near He $^*$ may contribute to an artificial reduction in the absorption line blue shift by up to 30 cm $^{-1}$ .