J. McKeever, A. Boca, A. D. Boozer, J. R. Buck, H. J. Kimble
备注：
5 pages, 4 figures (slightly longer version -- before editorial revisions)
发表信息：
Nature 425, 268-271 (2003), supplementary information available at http://www.nature.com/cgi-taf/DynaPage.taf?file=/nature/journal/v425/n6955/abs /nature01974_fs.html
Although conventional lasers operate with a large number of intracavity atoms, the lasing properties of a single atom in a resonant cavity have been theoretically investigated for more than a decade. Here we report the experimental realization of such a one-atom laser operated in a regime of strong coupling. Our experiment exploits recent advances in cavity quantum electrodynamics that allow one atom to be isolated in an optical cavity in a regime for which one photon is sufficient to saturate the atomic transition. In this regime the observed characteristics of the atom-cavity system are qualitatively different from those of the familiar many atom case. Specifically, we present measurements of intracavity photon number versus pump intensity that exhibit "thresholdless" behavior, and infer that the output flux from the cavity mode exceeds that from atomic fluorescence by more than tenfold. Observations of the second-order intensity correlation function demonstrate that our one-atom laser generates manifestly nonclassical light that exhibits both photon antibunching and sub-Poissonian photon statistics.
An atom laser is a hypothetical device which would produce an atomic field analogous to the electromagnetic field of a photon laser. Here I argue that for this analogy to be meaningful it is necessary to have a precise definition of a laser which applies equally to photon or atom lasers. The definition I propose is based upon the principle that the output of a laser is well-approximated by a classical wave of fixed intensity and phase. This principle yields four quantitative conditions which the output of a device must satisfy in order for that device to be considered a laser. While explaining…
Entanglement of remote atom lasers is obtained via quantum state transfer technique from lights to matter waves in a five-level $M$-type system. The considered atom-atom collisions can yield an effective Kerr susceptibility for this system and lead to the self- and cross- phase modulation between the two output atom lasers. This effect results in generation of entangled states of output fields. Particularly, under different conditions of space-dependent control fields, the entanglement of atom lasers and of atom-light fields can be obtained, respectively. Furthermore, based on the Bell-state m…
A method to create paired atom laser beams from a metastable helium atom laser via four-wave mixing is demonstrated. Radio frequency outcoupling is used to extract atoms from a Bose Einstein condensate near the center of the condensate and initiate scattering between trapped and untrapped atoms. The unequal strengths of the interactions for different internal states allows an energy-momentum resonance which leads to the creation of pairs of atoms scattered from the zero-velocity condensate. The resulting scattered beams are well separated from the main atom laser in the 2-dimensional transvers…
We propose a scheme to obtain soliton atom laser with nonclassical atoms based on quantum state transfer process from light to matter waves in nonlinear case, which may find novel applications in, e.g., an atom interferometer. The dynamics of the atomic gray solitons and the accompanied frequency chirp effect are discussed.
We show that if the laser is intense enough, it may always ionize an atom or induce transitions between discrete energy levels of the atom, no matter what is its frequency. It means in the quantum transition of an atom interacting with an intense laser of circular frequency $ω$, the energy difference between the initial and the final states of the atom is not necessarily being an integer multiple of the quantum energy $\hbarω$. The absorption spectra become continuous. The Bohr condition is violated. The energy of photoelectrons becomes light intensity dependent in the intense laser photoelect…
We study theoretically the decoherence of a gas of bosonic atoms induced by the interaction with a largely detuned laser beam. It is shown that for a standing laser beam decoherence coincides with the single-particle result. For a running laser beam many-particle effects lead to significant modifications.
We present a fully quantum mechanical treatment of a single mode atom laser including pumping and output coupling. By ignoring atom-atom interactions, we have solved this model without making the Born-Markov approximation. We find substantially less gain narrowing than is predicted under that approximation.
We analyze two configurations for laser cooling of neutral atoms whose internal states store qubits. The atoms are trapped in an optical lattice which is placed inside a cavity. We show that the coupling of the atoms to the damped cavity mode can provide a mechanism which leads to cooling of the motion without destroying the quantum information.
We demonstrate broadband laser cooling of atomic ions in an rf trap using ultrafast pulses from a modelocked laser. The temperature of a single ion is measured by observing the size of a time-averaged image of the ion in the known harmonic trap potential. While the lowest observed temperature was only about 1 K, this method efficiently cools very hot atoms and can sufficiently localize trapped atoms to produce near diffraction-limited atomic images.
We discuss radiative corrections to an atomic two-level system subject to an intense driving laser field. It is shown that the Lamb shift of the laser-dressed states, which are the natural state basis of the combined atom-laser system, cannot be explained in terms of the Lamb shift received by the atomic bare states which is usually observed in spectroscopic experiments. In the final part, we propose an experimental scheme to measure these corrections based on the incoherent resonance fluorescence spectrum of the driven atom.
We study the scattering of two-level atoms at narrow laser fields, modeled by a $δ$-shape intensity profile. The unique properties of these potentials allow us to give simple analytic solutions for one or two field zones. Several applications are studied: a single $δ$-laser may serve as a detector model for atom detection and arrival-time measurements, either by means of fluorescence or variations in occupation probabilities. We show that, in principle, this ideal detector can measure the particle density, the quantum mechanical flux, arrival time distributions or local kinetic energy densitie…
This paper analyzes coherent backscattering of intense laser light by two randomly placed distant atoms. Starting from the general two-atom master equation, we analytically derive the elastic and inelastic background and interference components of the double scattering spectrum. By expressing the final results in terms of single-atom observables, the two-atom problem is shown to be equivalent to a description in terms of single atoms under bichromatic driving.
We give a detailed derivation of the master equation description of the coherent backscattering of laser light by cold atoms. In particular, our formalism accounts for the nonperturbative nonlinear response of the atoms when the injected intensity saturates the atomic transition. Explicit expressions are given for total and elastic backscattering intensities in the different polarization channels, for the simplest nontrivial multiple scattering scenario of intense laser light multiply scattering from two randomly placed atoms.
We present a nonperturbative treatment of coherent backscattering of intense laser light from cold atoms, and predict a nonvanishing backscattering signal even at very large intensities, due to the constructive (self-)interference of inelastically scattered photons.
We formulate a wave atom optics theory of the Collective Atomic Recoil Laser, where the atomic center-of-mass motion is treated quantum mechanically. By comparing the predictions of this theory with those of the ray atom optics theory, which treats the center-of-mass motion classically, we show that for the case of a far off-resonant pump laser the ray optics model fails to predict the linear response of the CARL when the temperature is of the order of the recoil temperature or less. This is due to the fact that in theis temperature regime one can no longer ignore the effects of matter-wave di…
Different laser devices working as ``atom diodes'' or ``one-way barriers'' for ultra-cold atoms have been proposed recently. They transmit ground state level atoms coming from one side, say from the left, but reflect them when they come from the other side. We combine a previous model, consisting of the stimulated Raman adiabatic passage (STIRAP) from the ground to an excited state and a state-selective mirror potential, with a localized quenching laser which produces spontaneous decay back to the ground state. This avoids backwards motion, provides more control of the decay process and theref…
We discuss the use of the Born and Markov approximations in describing the dynamics of an atom laser. In particular, we investigate the applicability of the quantum optical Born-Markov master equation for describing output coupling. We derive conditions based on the atomic reservoir, and atom dispersion relations for when the Born-Markov approximations are valid and discuss parameter regimes where these approximations fail in our atom laser model. Differences between the standard optical laser model and the atom laser are due to a combination of factors, including the parameter regimes in whic…
We investigate the effect of a laser shining perpendicularly to a waveguide channeling two-level atoms. For weak transversal coupling the excitation of transverse atomic levels occurs at avoided crossings associated with "Rabi resonances" in which the Rabi frequency coincides with the transition frequency between the transverse levels.
We propose a feasible scheme to create two spatially separated atomic and molecular beams from an atomic Bose-Einstein condensate by combining the Raman-type atom laser output and the two-color photo-association processes. We examine the quantum dynamics and statistical properties of the system under short-time limits, especially the quadrature-squeezed and mode-correlated behaviors of two output beams for different initial state of the condensate. The possibility to generate the entangled atom-molecule lasers by an optical technique was also discussed.
We quantify the entanglement generated between an atom and a laser pulse in free space. We find that the entanglement calculated using a simple closed-system Jaynes-Cummings Hamiltonian is in remarkable agreement with a full open-system calculation, even though the free-space geometry is far from the strong coupling regime of cavity QED. We explain this result using a simple model in which the atom couples weakly to the laser while coupling strongly to the vacuum. Additionally we place an upper bound on the total entanglement between the atom and all paraxial modes using a quantum trajectories…
A two-mode single-atom laser is considered, with the aim of generating entanglement in macroscopic light. Two transitions in the four-level gain medium atom independently interact with the two cavity modes, while two other transitions are driven by control laser fields. Atomic relaxation as well as cavity losses are taken into account. We show that this system is a source of macroscopic entangled light over a wide range of control parameters and initial states of the cavity field.
A natural approach to measure the time of arrival of an atom at a spatial region is to illuminate this region with a laser and detect the first fluorescence photons produced by the excitation of the atom and subsequent decay. We investigate the actual physical content of such a measurement in terms of atomic dynamical variables, taking into account the finite width of the laser beam. Different operation regimes are identified, in particular the ones in which the quantum current density may be obtained.
A continuous atom laser will almost certainly have a linewidth dominated by the effect of the atomic interaction energy, which turns fluctuations in the condensate atom number into fluctuations in the condensate frequency. These correlated fluctuations mean that information about the atom number could be used to reduce the frequency fluctuations, by controlling a spatially uniform potential. We show that feedback based on a physically reasonable quantum non-demolition measurement of the atom number of the condensate in situ can reduce the linewidth enormously.
We analyse the effects of atom-atom collisions on collective laser cooling scheme. We derive a quantum Master equation which describes the laser cooling in presence of atom-atom collisions in the weak-condensation regime. Using such equation, we perform Monte Carlo simulations of the population dynamics in one and three dimensions. We observe that the ground-state laser-induced condensation is maintained in the presence of collisions. Laser cooling causes a transition from a Bose-Einstein distribution describing collisionally induced equilibrium,to a distribution with an effective zero tempera…
In this paper we show how to control the quantum laser atoms instability using IR radiation. The control can be achieved by controlling the scattering length constant via the infrared coupling constant. This method is applied in the scheme of a continuous CW laser and involves three occupation levels in the condensed atoms.This atoms in Lambda configuration the description of which is given by a Reformed Gross-Pitaevskii equation (RGPE), together with a rate equation.The system is taken to a nonconservative complex Ginzburg Landau equation (CGLE) description from where we use the Benjamin-Feir…
We propose an implementation of the quantum search algorithm of a marked item in an unsorted list of N items by adiabatic passage in a cavity-laser-atom system. We use an ensemble of N identical three-level atoms trapped in a single-mode cavity and driven by two lasers. In each atom, the same level represents a database entry. One of the atoms is marked by having an energy gap between its two ground states. Appropriate time delays between the two laser pulses allow one to populate the marked state starting from an initial entangled state within a decoherence-free adiabatic subspace. The time t…
We propose and analyse a scheme for measuring the quadrature statistics of an atom laser beam using extant optical homodyning and Raman atom laser techniques. Reversal of the normal Raman atom laser outcoupling scheme is used to map the quantum statistics of an incoupled beam to an optical probe beam. A multimode model of the spatial propagation dynamics shows that the Raman incoupler gives a clear signal of de Broglie wave quadrature squeezing for both pulsed and continuous inputs. Finally, we show that experimental realisations of the scheme may be tested with existing methods via measuremen…
Laser cooling of atomic motion enables a wide variety of technological and scientific explorations using cold atoms. Here we focus on the effect of laser cooling on the photons instead of on the atoms. Specifically, we show that non-interacting photons can thermalize with the atoms to a grand canonical ensemble with a non-zero chemical potential. This thermalization is accomplished via scattering of light between different optical modes, mediated by the laser cooling process. While optically thin modes lead to traditional laser cooling of the atoms, the dynamics of multiple scattering in optic…
We discuss a method to select the velocities of ultra-cold atoms with a modified Fabry-Perot type of device made of two effective barriers and a well created, respectively, by blue and red detuned lasers. The laser parameters may be used to select the peak and width of the transmitted velocity window. In particular, lowering the central well provides a peak arbitrarily close to zero velocity having a minimum but finite width. The low-energy atomic scattering off this laser device is parameterized and approximate formulae are found to describe and explain its behaviour.
We investigate the resonant quantum dynamics of a laser-pumped real or artificial two-level single-atom system embedded in a leaking microcavity. We found that for stronger laser-atom-cavity couplings the generated microcavity photons exhibit larger steady-state correlations. In particular, the second- and third-order photon correlation functions are greater than the corresponding ones obtained for an incoherent light source, respectively. Furthermore, the emitted microcavity photon flux is enhanced in comparison to weaker coupling cases.
We investigate a single laser driven atom trapped in a non-harmonic potential. We present the performance of ground-state laser cooling and Doppler cooling and the signatures of the center-of-mass motion in the power spectrum of the scattered light. In order to illustrate the results we provide two explicit examples for the confining potential: the infinite square well and the Morse potential.
The quantum dynamics of two distant H atoms excited by ultrashort and spatially shaped laser pulses is studied by the numerical solution of the non-Born-Oppenheimer time-dependent Schrödinger equation within a three-dimensional (3D) model, including the internuclear distance R and the two z coordinates of the electrons, z1 and z2. The two 1D hydrogen atoms, A and B, are assumed to be initially in their ground states with a large (but otherwise arbitrary) internuclear separation of R = 100 a.u. (5.29 nm). Two types of a spatial envelope of a laser field linearly po- larized along the z-axis are…
Two-flavor atom laser in a vortex state is obtained and analyzed via electromagnetically induced transparency (EIT) technique in a five-level $M$ type system by using two probe lights with $\pm z$-directional orbital angular momentum $\pm l\hbar$, respectively. Together with the original transfer technique of quantum states from light to matter waves, the present result can be extended to generate continuous two-flavor vortex atom laser with non-classical atoms.
The laser cooling of atoms is a result of the combined effect of doppler shift, light shift and polarization gradient. These are basically undesirable phenomena. However, they combine gainfully in realizing laser cooling and trapping of the atoms. In this paper we discuss the laser cooling of atoms in the presence of the squeezed light with the decay of atomic dipole moment into noisy quadrature. We show that the higher decay rate of the atomic dipole moment into the noisy quadrature, which is also an undesirable effect, may contribute in realizing larger cooling force vis-a-vis normal laser l…
We propose a scheme that allows to laser cool trapped atoms to the ground state of a one-dimensional confining potential. The scheme is based on the creation of a dark state by designing the laser profile, so that the hottest atoms are coherently pumped to another internal level, and then repumped back. The scheme works beyond the Lamb-Dicke limit. We present results of a full quantum treatment for a one-dimensional model.
We consider ultracold atoms in a far detuned optical lattice orientated across a high-Q optical resonator. Applying an external driving laser to the atoms, which is red detuned from the cavity mode by one vibrational quantum, induces cavity-enhanced sideband cooling. For a dense and cold enough atomic ensemble we predict an oscillation threshold for optical Raman sideband lasing concurrent with coherent matter-wave amplification. Above this oscillation threshold photons and atoms in the lowest band are dominantly created pairwise via stimulated emission with a strong suppression of competing s…
We present a mechanism for cooling atoms by a laser beam reflected from a single mirror. The cooling relies on the dipole force and thus in principle applies to arbitrary refractive particles including atoms, molecules, or dielectric spheres. Friction and equilibrium temperatures are derived by an analytic perturbative approach. Finally, semiclassical Monte-Carlo simulations are performed to validate the analytic results.
In this paper, we present a method to generate continuous-variable-type entangled states between photons and atoms in atomic Bose-Einstein condensate (BEC). The proposed method involves an atomic BEC with three internal states, a weak quantized probe laser and a strong classical coupling laser, which form a three-level Lambda-shaped BEC system. We consider a situation where the BEC is in electromagnetically induced transparency (EIT) with the coupling laser being much stronger than the probe laser. In this case, the upper and intermediate levels are unpopulated, so that their adiabatic elimina…
Demonstrating that despite loss processes, Bose-Einstein condensates can be formed in steady state is a prerequisite for obtaining a coherent beam of atoms in a continuous-wave atom laser. In this paper we propose a method for loading atoms into the thermal component of a Bose condensed cloud confined in a magnetic trap. This method is aimed at allowing steady state dynamics to be achieved. The proposed scheme involves loading atoms into the conservative magnetic potential using the spontaneous emission of photons. We show that the probability for the reabsorption of these photons may be small…
We have demonstrated and modeled a simple and efficient method to transfer atoms from a first Magneto-Optical Trap (MOT) to a second one. Two independent setups, with cesium and rubidium atoms respectively, have shown that a high power and slightly diverging laser beam optimizes the transfer between the two traps when its frequency is red-detuned from the atomic transition. This pushing laser extracts a continuous beam of slow and cold atoms out of the first MOT and also provides a guiding to the second one through the dipolar force. In order to optimize the transfer efficiency, the dependence…
We deduce the coherent backscattering signal from two distant laser-driven atoms using single-atom equations. In contrast to the standard master equation treatment, this new approach is suitable for the generalization to a large number of atomic scatterers.
We theoretically study the focusing of a quasi-continuous atom laser beam of rubidium-85 ($^{85}$Rb). A two-sate model analysis based on the Gross-Pitaevskii equation is used which comprises the effects of two-body atom-atom interactions and three-body recombination losses. Utilizing optical focusing potentials such as harmonic potentials, the essential factors such as the width, peak density and atom loss rate of the focused atom laser beam profile are investigated. Our analysis predicts that using an atom laser offers a dramatic improvement in resolution of up to $8$ nm.
The use of Raman laser generated by modulation for light-pulse atom interferometer allows to have a laser system more compact and robust. However, the additional laser frequencies generated can perturb the atom interferometer. In this article, we present a precise calculation of the phase shift induced by the additional laser frequencies. The model is validated by comparison with experimental measurements on an atom gravimeter. The uncertainty of the phase shift determination limits the accuracy of our compact gravimeter at 8.10^-8 m/s^2. We show that it is possible to reduce considerably this…
We present a novel, ultra-bright atom-laser and ultra-cold thermal atom beam. Using rf-radiation we strongly couple the magnetic hyperfine levels of 87Rb atoms in a magnetically trapped Bose-Einstein condensate. At low rf-frequencies gravity opens a small hole in the trapping potenital and a well collimated, extremely bright atom laser emerges from just below the condensate. As opposed to traditional atom lasers based on weak coupling, this technique allows us to outcouple atoms at an arbitrarily large rate. We demonstrate an increase in flux per atom in the BEC by a factor of sixteen compared…
We introduce a scheme for creating continuous variable entanglement between an atomic beam and an optical field, by using squeezed light to outcouple atoms from a BEC via a Raman transition. We model the full multimode dynamics of the atom laser beam and the squeezed optical field, and show that with appropriate two-photon detuning and two-photon Rabi frequency, the transmitted light is entangled in amplitude and phase with the outcoupled atom laser beam. The degree of entanglement is controllable via changes in the two-photon Rabi frequency of the outcoupling process.
We examine the properties of an atom laser produced by outcoupling from a Bose-Einstein condensate with squeezed light. We model the multimode dynamics of the output field and show that a significant amount of squeezing can be transfered from an optical mode to a propagating atom laser beam. We use this to demonstrate that two-mode squeezing can be used to produce twin atom laser beams with continuous variable entanglement in amplitude and phase.
We show that two groups of slow two-level atoms in a weak resonant laser field, are entangled. The considered groups can be separated by a macroscopic distance, and be parts of a larger atomic ensemble. In a dilute regime, for two very distant groups of atoms, in a plane wave laser beam, we determine the maximum attainable entanglement negativity, and a laser intensity below which they are certainly entangled. They both decrease with increasing distance between the two groups, but increase with enlarging groups sizes. As a consequence, for given laser intensity, far separated groups of atoms a…
Atom interferometry is the most successful technique for precision metrology. However, current interferometers using ultracold atoms allows one to probe the interference pattern only momentarily and has finite duty cycle, resulting in an aliasing effect and a low-bandwidth measurement -- also known as Dick effect. Interferometry with a continuous-wave atom laser shows promise in overcoming these limitations due a continuous monitoring of the interference pattern. In this work, we demonstrate a key step towards such an interferometry by demonstrating a diffraction of an `atom laser' in the Rama…
A spectroscopic application of the atom laser is suggested. The spectroscopy termed 2PACC employs the coherent properties of matter-waves from a two pulse atom laser. These waves are employed to control a gas-surface chemical recombination reaction. The method is demonstrated for an Eley-Rideal reaction of a hydrogen or alkali atom-laser pulse where the surface target is an adsorbed hydrogen atom. The reaction yields either a hydrogen or alkali hydride molecule. The desorbed gas phase molecular yield and its internal state is shown to be controlled by the time and phase delay between two atom-…
We consider the effects of the trap environment on the atomic and optical quantum statistical properties and on the atom-photon correlations in the Collective Atomic-Recoil Laser. Atomic and optical statistical properties, as well as the atom-photon correlations are dependent on the optical field intensity and phase. In particular, depending on the values of the optical field intensity and phase, the fields statistics varies from coherent to superchaotic.
The linewidth of an atom laser can be limited by excitation of higher energy modes in the source Bose-Einstein condensate, energy shifts in that condensate due to the atomic interactions, or phase diffusion of the lasing mode due to those interactions. The first two are effects that can be described with a semiclassical model, and have been studied in detail for both pumped and unpumped atom lasers. The third is a purely quantum statistical effect, and has been studied only in zero dimensional models. We examine an unpumped atom laser in one dimension using a quantum field theory using stochas…
The effect of collectivity on the loading of an atom laser via optical pumping is discussed. In our model, atoms in a beam are laser-excited and subsequently spontaneously decay into a trapping state. We consider the case of sufficiently high particle density in the beam such that the spontaneous emission is modified by the particle interaction. We show that the collective effects lead to a better population of the trapping state over a wide range of system parameters, and that the second order correlation function of the atoms can be controlled by the applied laser field.
We report on theoretical and numerical study of propagation of atomic beams crossing a detuned standing-wave laser beam in the geometric optics limit. The interplay between external and internal atomic degrees of freedom is used to manipulate the atomic motion along the optical axis by light. By adjusting the atom-laser detuning, we demonstrate how to focus, split and scatter atomic beams in a real experiment. The novel effect of chaotic scattering of atoms at a regular near-resonant standing wave is found numerically and explained qualitatively. Some applications of the effects found are disc…
Bad cavity lasers are experiencing renewed interest in the context of active optical frequency standards, due to their enhanced robustness against fluctuations of the laser cavity. The gain medium would consist of narrow-linewidth atoms, either trapped inside the cavity or intersecting the cavity mode dynamically. A series of effects like the atoms finite velocity distribution, atomic interactions, or interactions of realistic multilevel atoms with auxiliary or stray fields can lead to an inhomogeneous broadening of the atomic gain profile. This causes the emergence of instable regimes of lase…
The stationary state of a single-atom (single-qubit) laser is shown to be a phase-averaged nonlinear coherent state - an eigenstate of a specific deformed annihilation operator. The solution found for the stationary state is unique and valid for all regimes of the single-qubit laser operation. We have found the parametrization of the deformed annihilation operator which provides superconvergence in finding the stationary state by iteration. It is also shown that, contrary to the case of the usual laser with constant Einstein coefficients describing transition probabilities, for the single-atom…
We study the properties of an atom laser beam derived from a Bose-Einstein condensate using three different outcouplers, one based on multi-state radio frequency transitions and two others based on Raman transitions capable of imparting momentum to the beam. We first summarize the differences that arise in such systems, and how they may impact on the use of an atom laser in interferometry. Experimentally, we examine the formation of a bound state in all three outcouplers, a phenomenon which limits the atom laser flux, and find that a two-state Raman outcoupler is the preferred option for high …
We present a diagrammatic derivation of the coherent backscattering spectrum from two two-level atoms using the pump-probe approach, wherein the multiple scattering signal is deduced from single-atom responses, and provide a physical interpretation of the single-atom building blocks.
We report on the observation of interference of a series of atom lasers. A comb-like array of coherent atomic beams is generated by outcoupling atoms from distinct Bose-Einstein condensates confined in the independent sites of a mesoscopic optical lattice. The observed interference signal arises from the spatial beating of the overlapped atom laser beams, which is sampled over a vertical region corresponding to 2 ms of free fall time. The average relative de Broglie frequency of the atom lasers was measured.
