Entanglement swapping: entangling atoms that never interacted

In this paper we discuss four different proposals of entangling atomic states of particles which have never interacted. The experimental realization proposed makes use of the interaction of Rydberg atoms with a micromaser cavity prepared in either a coherent state or in a superposition of the field Fock states |0? and |1?. We consider atoms in either a three-level cascade or lambda configuration.     

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.     

Emission Spectra of a Two-level Atom Under the Presence of Another Two-level Atom

Abstract

We investigate the spectrum of light emitted by a two-level atom interacting with another two-level atom inside an ideal cavity within the frame of generalized Jaynes-Cummings model. The influence of various ratios of the coupling constants of the atoms to the field on the spectrum of the emitted light is studied in detail for the case when the atoms are supposed to be initially in the excited state and the field in a Fock state as well as their superposition.     

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.     

Atomic interference in the micromaser and statistical properties of the micromaser field

Abstract

In this paper we report on atomic interferometry in the micromaser. The atomic inversion is recorded while scanning the cavity frequency across the atomic resonance. For high pump rates, interference patterns are observed on the low-frequency wing of the maser line. The interferences are due to the non-adiabatic mixing of dressed states of the atoms at the entrance and exit holes of the maser cavity, leading to a Ramsey-type two-field interaction. Furthermore, statistical properties of the maser field are investigated via a measurement of the statistics of the pump atoms that leave the maser cavity. Theoretical expressions for the time dependence of the Fano–Mandel parameter Q _A(t) are compared with the experimental data. We demonstrate, that metastability of the maser field and atomic interference strongly influence the approach to a steady-state value of Q _A(t).     

Field-dipole orientation mechanism and higher order modes in atom guides

Abstract

In cavity quantum electrodynamics (CQED), cavity size, dipole position and dipole orientation are the main factors controlling cavity effects, for example, suppression and enhancement of spontaneous emission. However, the dynamical effects of dipole orientation in CQED have, to date, remained largely unexplored, with most treatments simply concentrating on two (or three) orthogonal directions to illustrate the variations of CQED effects with dipole orientation. No mechanism which determines the evolution of the dipole orientation has been put forward to describe typical situations where atoms move in the field of an excited cavity mode. We emphasize here that in the presence of a cavity mode, the average dipole orientation is automatically determined at every point to be parallel to the direction of the electric field vector of the cavity mode. Besides giving rise to a single value for the spontaneous emission rate, this mechanism is shown to have important consequences for the dynamics of atoms in atom guides. In particular, it determines the average trapping potential distributions and the average radiation forces which guide the atoms along a cylindrical cavity. The effects of the field-dipole orientation mechanism are illustrated with reference to typical situations involving sodium atoms in sub-micron cylindrical guides. The role of a higher order cavity mode of the cylinder in the dynamics is highlighted in terms of its influence on the rotational and vibrational motions in such guides.     

Effects of cavity-field statistics on atomic entanglement in a two-mode Jaynes–Cummings model with intensity-dependent coupling

We study the entanglement properties of a pair of two-level Rydberg atoms passing one after another into a lossless cavity with two modes. The atoms interact with the cavity field via an intensity-dependent, non-degenerate two-photon transition. The initial joint state of two successive atoms that enter the cavity is unentangled. Interactions mediated by the two-mode cavity photon field result in the final two-atom mixed entangled type state. The entanglement of formation of the joint two-atom state as a function of the Rabi angle, gt, is calculated for the two-mode Fock state field, coherent field, and thermal field, respectively, inside the cavity. The change in the magnitude of atomic entanglement with cavity photon number in two modes has been studied.     

Periodic Squeezing in the Tavis-Cummings Model

Abstract

By utilizing our previous operator solution [17], we have investigated the squeezing in the radiation field of the Tavis-Cummings model (collective N ? 1 two-level atoms interacting with a resonant single cavity quantized mode). With field and atoms initially in coherent field state strong or weak and atomic coherent state (of few excited atoms), periodic time-dependent squeezing in the field and the macroscopic polarization is expressed in terms of Jacobian elliptic functions of the first kind. The statistical investigations are carried out for the quasiprobability distribution functions (Wigner function and Q function). The distribution function of the field quadrature has a variance less (greater) than that for a coherent state if this quadrature is squeezed (unsqueezed).     

Generating non-classical light inside an optical cavity by depositing photons

The creation of non-classical states of light is an interesting problem, that we solve sending atoms through an optical cavity. We show that it is possible to add or subtract many photons from a cavity field by interacting it resonantly with a two-level atom. The atom, after entangling with the field inside the cavity and exiting it, may be measured in one of the Schmidt states, producing a multiphoton process (in the sense that can add or annihilate more photons than a single transition allows), i.e. adding or subtracting several photons from the cavity field. By plotting the quadratures and the Husimi Q-function, we also show that the non-classical state produced by such measurements is a squeezed state.     

Quasi mode theory of macroscopic canonical quantization in quantum optics and cavity quantum electrodynamics

Abstract

A macroscopic, canonical quantization of the EM field and radiating atom system in quantum optics and cavity QED involving classical, linear optical devices, based on expanding the vector potential in terms of quasi mode functions is presented. The quasi mode functions approximate the true mode functions for the device, and are obtained by solving the Helmholtz equation for an idealized spatially dependent electric permittivity function describing the device. The Hamiltonian for the EM field and radiating atom system is obtained in multipolar form and the quantum EM field is found to be equivalent to a set of quantum harmonic oscillators, one oscillator per quasi mode. However, unlike true mode theory where the quantum harmonic oscillators are uncoupled, in the quasi mode theory they are coupled and photon exchange processes can occur. Explicit expressions for the coupling constants are obtained. The interaction energy between the radiative atoms and the quantum EM field depends on the amplitudes of the quasi mode functions at the positions of the radiating atoms, similar to that for the true mode approach. The simpler forms for the quasi mode functions enable the atom-field interaction energy to be written in a form in which the atoms are only coupled to certain types of modes—for example cavity quasi modes, which are large inside the optical cavity. In such cases the escape of energy from excited atoms in the cavity can be pictured in quasi mode theory as a two step process—the atom de-excites and creates a photon in a cavity quasi mode, the photon in the cavity quasi mode is then lost and appears as a photon in an external quasi mode. In this process the first step occurs via the atom-cavity quasi mode interaction, the second through coupling between cavity and external quasi modes. This may be contrasted with the true mode approach, where the excited atom loses its energy and the photon is created in one of the true modes. As all true modes have non-zero amplitudes outside as well as inside the cavity, the escape of energy from excited atoms in the cavity is seen as a one step process. An application of the quasi mode theory to the quantum theory of the beam splitter is outlined. The unitary operator used to describe this device is a scattering operator, relating initial and long time values of annihilation, creation operators for pairs of incident and reflected modes, interpreted here as quasi modes.     

The phase evolution of a micromaser field without the rotating-wave approximation

Abstract

In a one-atom micromaser, the expression for the density matrix of the cavity field without the rotating-wave approximation (RWA) is derived using a perturbation method. The phase evolution of the cavity field is investigated without the RWA, and the results are compared with those within the RWA. It is shown that the virtual-photon processes make the symmetric phase distribution in the RWA asymmetric and cause additional quantum oscillation, which indicate the field's phase fluctuation and frequency shift. Virtual photons also cause an extra phase distribution to the field which is initially in a vacuum state. The unique characteristic of the phase properties in the course of forming a photon-number state is investigated. Other new phenomena such as the undamped oscillation of the phase variance against the injected atomic number are found.     

The dynamics of entanglement and quantum discord of two atoms in coupled cavities

We investigate the dynamics of quantum correlations such as entanglement and quantum discord between two noninteracting atoms, each of which is trapped inside one of two coupled cavities. We find that the cavity decay can induce both entanglement and quantum discord between the two atoms when they are initially prepared in doubly excited state. The result shows the sudden death and sudden birth of entanglement and robustness of the quantum discord to sudden death. It is also found that the doubly excited state is responsible for the sudden death of entanglement. Moreover, the sudden death of entanglement can be controlled by the intercavity hopping rate.     

Generation of photon number states on demand

Abstract

The widely discussed applications in quantum information and quantum cryptography require radiation sources capable of producing a fixed number of photons. This paper reviews the work performed in our laboratory to produce these fields on demand. Two different methods are discussed. The first is based on the one-atom maser or micromaser operating under the conditions of the so-called trapping states. In this situation the micromaser stabilises to a photon number state. Recently, we also succeeded in determining the Wigner function of a single-photon state. The second device, recently realized in our laboratory, uses a single trapped ion in an optical cavity.     

Cavity QED analog of spin

Abstract

Using the even and odd coherent states, we show that a single mode cavity field, prepared in a coherent state by a classical source and manipulated by both dispersive and resonant interactions with atoms, is analogous to a spin one-half particle interacting with Stern–Gerlach magnets where the parity of the field is the analog of spin. Because the number of photons in the cavity may be large, the system we describe can exhibit quantum effects on at least a mesoscopic scale. We show that entangled two and three cavity systems can be generated. The three cavity case can be used to demonstrate the contradiction between local realistic theories and quantum mechanics in the manner proposed by Greenberger, Horne and Zeilinger in 1989 [13].     

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.     

Conditional generation of non-classical states in a non-degenerate two-photon micromaser: Single-mode fock states preparation. II

Abstract

A conditional generation of single-mode Fock states in the framework of a non-degenerate two-photon micromaser theory is reported. The exact expression for the probability of success of the experiment is obtained. We show that it is possible to conjugate experimentally interesting values of this probability, with the generation of number states having a controllable high intensity. This objective is reached by constructing analytically detailed rules about the cavity state at t = 0 as well as the atom–field interaction times as functions of the available operating conditions. These rules play a central role in our Fock-state-building process, leading to an essential countering of the Stark-shift-induced detuning effects. The practical reliability of the proposal is carefully discussed from several points of view. Some possible applicative potentialities of our scheme are briefly pointed out.     

Highly Excited Hydrogen in Strong D.C. Electric Fields: Atomic Engineering

Abstract

We excite atomic hydrogen from the ground state via a three-photon process to high-lying excited states in the presence of strong d.c. electric fields. The external field is used to manipulate, control, and design specific atomic structures. We can construct nearly ‘one-dimensional’ atoms whose electronic distributions are highly extended along the field, and which may have enormous electric dipole moments (‘giant-dipole atoms’).     

Micromaser with Two-photon Absorber

Abstract

We demonstrate that operating a micromaser simultaneously on a one- and a two-photon transition leads to a variety of new physical effects. Using a two-photon absorber can substantially lower the stringent temperature requirements to generate states with a very narrow non-classical photon number distribution. In addition one gets a powerful measuring device to investigate dynamical properties of the micromaser field.     

Spectrum of a Micromaser with Kerr Nonlinearity

Abstract

We analyse the spectrum of a micromaser with a Kerr-type nonlinearity in its cavity. We show that the intracavity Kerr nonlinearity has significant effects on the spectrum leading to narrowing of the subnatural linewidth and frequency-shifts.