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We propose an experimental scheme for the measurement of entanglement between two two-level atoms. Our scheme requires one of the two entangled atoms to interact with a cavity field dispersively, and we show that by measuring the zero time-delay second-order coherence function of the cavity field, one can measure the concurrence of an arbitrary Bell-like atomic two-qubit state. As our scheme requires only one of the atoms to interact with the measured cavity, the entanglement quantification becomes independent of the location of the other atom. Therefore, our scheme can have important implications for entanglement quantification in distributed quantum systems., Accepted in Annalen der Physik

This theoretical work initiates contact between two frontier disciplines of physics, namely, atomic superfluid rotation and cavity optomechanics. It considers an annular Bose-Einstein condensate, which exhibits dissipationless flow and is a paradigm of rotational quantum physics, inside a cavity excited by optical fields carrying orbital angular momentum. It provides the first platform that can sense ring Bose-Einstein condensate rotation with minimal destruction, in situ and in real time, unlike demonstrated techniques, all of which involve fully destructive measurement. It also shows how light can actively manipulate rotating matter waves by optomechanically entangling persistent currents. Our work opens up a novel and useful direction in the sensing and manipulation of atomic superflow.

Phonon lasers are mechanical analogues of the ubiquitous optical laser and have been realized in a variety of contexts1–12. However, no such demonstration exists for mesoscopic levitated optomechanical systems, which are emerging as important platforms for conducting fundamental tests of quantum mechanics13–15 and gravity16, as well as for developing sensing modalities that couple mechanical motion to electron spin17–20 and charge21. Inspired by the pioneering work of Arthur Ashkin on optical tweezers22,23, we introduce a mesoscopic, frequency-tunable phonon laser based on the centre-of-mass oscillation of a silica nanosphere levitated in an optical tweezer under vacuum. Unlike previous levitated realizations, our scheme is general enough to be used on single electrons, liquid droplets or even small biological organisms24. Our device thus provides a pathway for a coherent source of phonons on the mesoscale that can be applied to both fundamental problems in quantum mechanics as well as tasks of precision metrology25–27. A phonon laser based on an optically levitated silica nanosphere is demonstrated. A lasing threshold—a phase transition from Brownian motion to coherent oscillation—is observed when the modulation depth of the trapping beam power is increased.

We present theoretical and experimental investigations of higher order correlations of mechanical motion in the recently demonstrated optical tweezer phonon laser, consisting of a silica nanosphere trapped in vacuum by a tightly focused optical beam [Nat. Photonics 13, 402 (2019)10.1038/s41566-019-0395-5]. The nanoparticle phonon number probability distribution is modeled with the master equation formalism in order to study its evolution across the lasing threshold. Up to fourth-order equal-time correlation functions are then derived from the probability distribution. Subsequently, the master equation is transformed into a nonlinear quantum Langevin equation for the trapped particle’s position. This equation yields the non-equal-time correlations, also up to fourth order. Finally, we present experimental measurements of the phononic correlation functions, which are in good agreement with our theoretical predictions. We also compare the experimental data to existing analytical Ginzburg-Landau theory where we find only a partial match.

We demonstrate that the conservation of extremal ellipticity for an astigmatic Gaussian beam propagating in a rotationally invariant medium, for example, an arbitrary sequence of free space propagation and stigmatic lenses, initially identified by Lo et al. (2017), is a direct consequence of the conservation of orbital angular momentum (OAM) of the beam. We derive explicit analytical expressions for the first few non-zero moments of the beam OAM and show that, apart from fundamental constants, they depend only on the beam’s extremal ellipticity. This unexpected connection uncovers the actual origin of a new propagation invariant, namely extremal ellipticity, for a broad class of coherent, single-mode Gaussian beams. We expect this principle to find use in various applications where spot circularity along an extended region of the beam is essential; such as laser micromachining, imaging, optical trapping, and inertial confinement fusion.

We theoretically describe a levitated Mie particle phonon laser, obtained by coupling the particle oscillations to a whispering gallery mode via laser radiation. We show that ultrasensitive force sensing can be performed using this platform.

We theoretically explore a quantum memory using a single nanoparticle levitated in an optical dipole trap and subjected to feedback cooling. This protocol is realized by storing and retrieving a single-photon quantum state from a mechanical mode in levitated cavityless optomechanics. We describe the effectiveness of the photon-phonon-photon transfer in terms of the fidelity, the Wigner function, and the zero-delay second-order autocorrelation function. For experimentally accessible parameters, our numerical results indicate robust conversion of the quantum states of the input signal photon to those of the retrieved photon. We also show that high fidelity single-photon wavelength conversion is possible in the system as long as intense control pulses shorter than the mechanical damping time are used. Our work opens up the possibility of using levitated optomechanical systems for applications of quantum information processing.

We propose a method to generate transiently nonclassical motional states in a levitated optomechanical system. The nonclassicality arises from a nonlinearity induced by coupling the mechanical motion of a nanodiamond carrying a nitrogen-vacancy center with its spin degrees of freedom using a second-order magnetic field gradient (MFG). We employ a Fokker–Planck equation for the Wigner distribution to study the effect of the induced nonlinearity on the dynamics of the system. The time evolution of the Wigner distribution reveals the transient generation of several nonclassical states. The presence of these states is also confirmed by the negativity of the Wigner function. We expect such nonclassical states to have potential applications in quantum information processing and quantum metrology.

Hollow-core photonic crystal fibers offer a versatile platform for developing cutting edge optical sensors through particle levitation. Here, the orbital angular momentum mode of such a fiber is utilized to rotate a dielectric nanoparticle, levitated inside the fiber via the gradient force. The rotation frequency, measured from the output intensity modulation caused by the particle rotation, enables sensing of the input power, core pressure, and particle size. Different types of particle dynamics can be obtained by using various orders of angular momentum modes supported by the fiber. At high input power, the system exhibits interesting nonlinear dynamics. Our proposal represents a versatile platform for fiber-based nanoparticle rotation sensing.

We theoretically consider light storage in a single nanoparticle levitated in an optical dipole trap and subjected to nonlinear feedback cooling. The storage protocol is realized by controlling the coupling between mechanical displacement and signal pulse by maneuvering the intensity of writing and readout pulses. The process involves writing and readout pulses at one mechanical frequency below the signal pulse. We demonstrate that during the writing pulse, a signal pulse is stored as a mechanical excitation of the nanoparticle oscillation. It is then shown that a readout pulse at later time can retrieve the stored optical information from the mechanical oscillator. A long storage lifetime of 2 ms is obtained in our system due to the absence of clamping losses. Further, we describe that our protocol can be used for wavelength conversion and shows a saturation in the conversion efficiency as a function of cooperativities of the writing and readout pulses. We also illustrate that the presence of linear feedback heating can lead to the amplification of the retrieved photon energy. Our prototype for light storage with levitated optomechanics can be used to explore the possibility of quantum memories for photonic states.

We propose a single phase-only optical element that transforms different orbital angular momentum (OAM) modes into localized spots at separated angular positions on a transverse plane. We refer to this element as an angular lens since it separates out OAM modes in a manner analogous to how a converging lens separates out transverse wave-vector modes at the focal plane. We also simulate the proposed angular lens using a spatial light modulator and experimentally demonstrate its working. Our work can have important implications for OAM-based classical and quantum communication applications., Comment: 5 pages, 5 figures

A phonon laser based on the center-of-mass oscillations of a silica nanosphere, levitated in an optical tweezer under vacuum, is proposed and developed. The observed dynamics are shown to result from stimulated emission of phonons.

In a region free of currents, magnetostatics can be described by the Laplace equation of a scalar magnetic potential, and one can apply the same methods commonly used in electrostatics. Here, we show how to calculate the general vector field inside a real (finite) solenoid, using only the magnitude of the field along the symmetry axis. Our method does not require integration or knowledge of the current distribution and is presented through practical examples, including a nonuniform finite solenoid used to produce cold atomic beams via laser cooling. These examples allow educators to discuss the nontrivial calculation of fields off-axis using concepts familiar to most students, while offering the opportunity to introduce themes of current modern research.

We analyze magnetometry using an optically levitated nanodiamond. We consider a configuration where a magnetic field gradient couples the mechanical oscillation of the diamond with its spin degree of freedom provided by a Nitrogen vacancy center. First, we investigate measurement of the position spectrum of the mechanical oscillator. We find that conditions of ultrahigh vacuum and feedback cooling allow a magnetic field gradient sensitivity of 1 $\mu$Tm$^{-1}$/$\sqrt{\mbox{Hz}}$. At high pressure and room temperature, this sensitivity degrades and can attain a value of the order of 100 $m$Tm$^{-1}$/$\sqrt{\mbox{Hz}}$. Subsequently, we characterize the magnetic field gradient sensitivity obtainable by maneuvering the spin degrees of freedom using Ramsey interferometry. We find that this technique can offer photon-shot noise and spin-projection noise limited magnetic field gradient sensitivity of 100 $\mu$Tm$^{-1}$/$\sqrt{\mbox{Hz}}$. We conclude that this hybrid levitated nanomechanical magnetometer provides a favorable and versatile platform for sensing applications.

Second quantization is a powerful technique for describing quantum mechanical processes in which the number of excitations of a single particle is not conserved. A textbook example of second quantization is the presentation of the simple harmonic oscillator in terms of creation and annihilation operators, which, respectively, represent addition or removal of quanta of energy from the oscillator. Our aim in this article is to bolster this textbook example. Accordingly, we explore the physics of coupled second-quantized oscillators. These explorations are phrased as exactly solvable eigenvalue problems, the mathematical structure providing a framework for the physical understanding. The examples we present can be used to enhance the discussion of second-quantized harmonic oscillators in the classroom, to make a connection to the classical physics of coupled oscillators, and to acquaint students with systems employed at the frontiers of contemporary physics research.

We propose a new configuration for realizing torsional optomechanics: an optically trapped windmill-shaped dielectric interacting with Laguerre-Gaussian cavity modes containing both angular and radial nodes. In contrast to existing schemes, our method can couple mechanical oscillators smaller than the optical beam waist to the in-principle unlimited orbital angular momentum that can be carried by a single photon, and thus generate substantial optomechanical interactions. Combining the advantages of small mass, large coupling, and low clamping losses, our work conceptually opens the way for the observation of quantum effects in torsional optomechanics., 8 pages, 5 figures

Optically levitated nanoparticles have recently emerged as versatile platforms for investigating macroscopic quantum mechanics and enabling ultrasensitive metrology. In this article we theoretically consider two damping regimes of an optically levitated nanoparticle cooled by cavityless parametric feedback. Our treatment is based on a generalized Fokker-Planck equation derived from the quantum master equation presented recently and shown to agree very well with experiment [1]. For low damping, we find that the resulting Wigner function yields the single-peaked oscillator position distribution and recovers the appropriate energy distribution derived earlier using a classical theory and verified experimentally [2]. For high damping, in contrast, we predict a double-peaked position distribution, which we trace to an underlying bistability induced by feedback. Unlike in cavity-based optomechanics, stochastic processes play a major role in determining the bistable behavior. To support our conclusions, we present analytical expressions as well as numerical simulations using the truncated Wigner function approach. Our work opens up the prospect of developing bistability-based devices, characterization of phase-space dynamics, and investigation of the quantum-classical transition using levitated nanoparticles., Comment: 11 pages, 11 figures. Comments are welcome

Nonclassical states of macroscopic objects are promising for ultrasensitive metrology as well as testing quantum mechanics. In this work, we investigate dissipative mechanical quantum state engineering in an optically levitated nanodiamond. First, we study single-mode mechanical squeezed states by magnetically coupling the mechanical motion to a dressed three-level system provided by a Nitrogen-vacancy center in the nanoparticle. Quantum coherence between the dressed levels is created via microwave fields to induce a two-phonon transition, which results in mechanical squeezing. Remarkably, we find that in ultrahigh vacuum quantum squeezing is achievable at room temperature with feedback cooling. For moderate vacuum, quantum squeezing is possible with cryogenic temperature. Second, we present a setup for two mechanical modes coupled to the dressed three levels, which results in two-mode squeezing analogous to the mechanism of the single-mode case. In contrast to previous works, our study provides a deterministic method for engineering macroscopic squeezed states without the requirement for a cavity., Comment: 13 pages, 11 figures. Comments are welcome!

A quantum harmonic oscillator coupled to a two-level system provides a tractable model of many physical systems from atoms in an optical cavity, to superconducting qubits coupled to an oscillator, to quantum dots in a photonic crystal. When the system experiences damping, the problem becomes considerably more complicated. We demonstrate how to gain insight by drawing analogies to classical damping. Specifically, we show how a quantum harmonic oscillator coupled to a damped two-level system can display two types of frictional behavior, corresponding to classical motion in a fluid and motion on a rough surface. We further show that this system can be tuned continuously between these two regimes.

Gaseous Bose-Einstein condensates (BECs) have become an important test bed for studying the dynamics of quantized vortices. In this work we use two-photon Doppler sensitive Bragg scattering to study the rotation of sodium BECs. We analyze the microscopic flow field and present laboratory measurements of the coarse-grained velocity profile. Unlike time-of-flight imaging, Bragg scattering is sensitive to the direction of rotation and therefore to the phase of the condensate. In addition, we have non-destructively probed the vortex flow field using a sequence of two Bragg pulses., 13 pages, 5 figures. Invited paper submitted to a special issue on "Nonlinear Waves" of the (Elsevier) journal 'Math. Comput. Simul.', for participants in the 4th IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena (2005). Visit our website at http://www.physics.gatech.edu/chandra for additional information

In this article we present a concrete proposal for spin squeezing the cold ground-state polar paramagnetic molecule OH, a system currently under fine control in the laboratory. In contrast to existing work, we consider a single, noninteracting molecule with angular momentum greater than $1/2$. Starting from an experimentally relevant effective Hamiltonian, we identify an adiabatic regime where different combinations of static electric and magnetic fields can be used to realize the single-axis twisting Hamiltonian of Kitagawa and Ueda [M. Kitagawa and M. Ueda, Phys. Rev. A 47, 5138 (1993)], the uniform field Hamiltonian proposed by Law et al. [C. K. Law, H. T. Ng, and P. T. Leung, Phys. Rev. A 63, 055601 (2001)], and a model of field propagation in a Kerr medium considered by Agarwal and Puri [G. S. Agarwal and R. R. Puri, Phys. Rev. A 39, 2969 (1989)]. We then consider the situation in which nonadiabatic effects are quite large and show that the effective Hamiltonian supports spin squeezing even in this case. We provide analytical expressions as well as numerical calculations, including optimization of field strengths and accounting for the effects of field misalignment. Our results have consequences for applications such as precision spectroscopy, techniques such as magnetometry, and stereochemical effects such as the orientation-to-alignment transition.

The stereochemical properties of the ultracold ground state OH molecule in the presence of electric and magnetic fields are currently of considerable interest. For example, relevant quantities such as molecular alignment and orientation, calculated numerically by using large basis sets, have lately appeared in the literature. In this work, based on our recent exact solution to an effective eight-dimensional matrix Hamiltonian for the molecular ground state, we present analytic expressions for the stereochemical properties of OH. Our results require the solution of algebraic equations only, agree well with the aforementioned fully numerical calculations, provide compact expressions for simple field geometries, allow ready access to relatively unexplored parameter space, and yield straightforwardly higher moments of the molecular axis distribution., 8 pages, 9 figures

We theoretically examine the optomechanical interaction between a rotating nanoparticle and an orbital angular momentum-carrying optical cavity mode. Specifically, we consider a dielectric nanosphere rotating uniformly in a ring-shaped optical potential inside a Fabry-Perot resonator. The motion of the particle is probed by a weak angular lattice, created by introducing two additional degenerate Laguerre-Gaussian cavity modes carrying equal and opposite orbital angular momenta. We demonstrate that the rotation frequency of the nanoparticle is imprinted on the probe optical mode, via the Doppler shift, and thus may be sensed experimentally using homodyne detection. We show analytically that the effect of the optical probe on the particle rotation vanishes in the regime of linear response, resulting in an accurate frequency measurement. We also numerically characterize the degradation of the measurement accuracy when the system is driven in the nonlinear regime. Our results are relevant to rotational Doppler velocimetry and to studies of rotational Brownian motion in a periodic lattice., 7 pages, 2 figures, to appear in JOSA B

Optically trapped nanoparticles have recently emerged as exciting candidates for tests of quantum mechanics at the macroscale and as versatile platforms for ultrasensitive metrology. Recent experiments have demonstrated parametric feedback cooling, nonequilibrium physics, and temperature detection, all in the classical regime. Here we provide the first quantum model for trapped nanoparticle cooling and force sensing. In contrast to existing theories, our work indicates that the nanomechanical ground state may be prepared without using an optical resonator; that the cooling mechanism corresponds to nonlinear friction; and that the energy loss during cooling is nonexponential in time. Our results show excellent agreement with experimental data in the classical limit, and constitute an underlying theoretical framework for experiments aiming at ground state preparation. Our theory also addresses the optimization of, and the fundamental quantum limit to, force sensing, thus providing theoretical direction to ongoing searches for ultra-weak forces using levitated nanoparticles., Comment: 8 pages, 5 figures, supplementary included. This version contains additional data and revised discussion

Development of a quantum master equation describing an optically trapped and cooled nanoparticle is presented. Using this model, we describe how the center of mass motion can be cooled to the quantum ground state.

We describe s-wave collisions between ultracold 23Na and 87Rb atoms in the presence of a magnetic field. For any collision input channel knowledge of the singlet and triplet intermolecular potentials [1] enables us to predict the variation in scattering lengths as a function of the magnetic field. We employ the Born-Oppenheimer approximation to predict several Feshbach resonances for 23Na87Rb. We also include a discussion of why these resonances are expected to be narrow as observed in the case of 87Rb2.

The emerging field of levitated optomechanics focuses on mesoscopic systems that are extremely well isolated from the environment and therefore offer unique tools for testing fundamental theories of physics as well as versatile platforms for supporting next-generation sensing technologies. The broad appeal of the subject as well as the novel possibilities it offers has attracted investigators to it from optics and photonics, magnetics, condensed matter physics, gravitational wave detection and astronomy, and low temperature physics. This special issue features contributions that describe various aspects at the cutting edge of the study and manipulation of levitated optomechanical systems, including experimental techniques, technological advances, and theoretical insights.

We consider theoretically a dielectric nanoparticle levitated in an optical ring trap inside a cavity and probed by an angular lattice, with all electromagnetic fields carrying orbital angular momentum. Analyzing the torsional motion of the particle about the cavity axis, we find that photon scattering from the trap beam plays an important role in the optomechanical system. First we show that the presence of the torque introduces an instability. Subsequently, we demonstrate that for bound motion near a stable equilibrium, varying the optical torque strength allows for tuning the linear optomechanical coupling. Finally, we indicate that the relative strengths of the linear and quadratic couplings can be detected directly by homodyning the cavity output. Our studies should be of interest to researchers exploring quantum mechanics using torsional optomechanics.

The OH molecule in its ground state presents a versatile platform for precision measurement and quantum information processing. These applications vitally depend on the accurate measurement of transition energies between the OH levels. Significant sources of systematic errors in these measurements are shifts based on the geometric phase arising from the magnetic and electric fields used for manipulating OH. In this article, we present these geometric phases for fields that vary harmonically in time, as in the Ramsey technique. Our calculation of the phases is exact within the description provided by our recent analytic solution of an effective Stark-Zeeman Hamiltonian for the OH ground state. This Hamiltonian has been shown to model experimental data accurately. We find that the OH geometric phases exhibit rich structure as a function of the field rotation rate. Remarkably, we find rotation rates where the geometric phase accumulated by a specific state is zero, or where the relative geometric phase between two states vanishes. We expect these findings to be of importance to precision experiments on OH involving time-varying fields. More specifically, our analysis quantitatively characterizes an important item in the error budget for precision spectroscopy of ground-state OH.

The ground electronic, vibrational and rotational state of the OH molecule is currently of interest as it can be manipulated by electric and magnetic fields for experimental studies in ultracold chemistry and quantum degeneracy. Based on our recent exact solution of the corresponding effective Stark-Zeeman Hamiltonian, we present an analytical study of the crossings and avoided crossings in the spectrum. These features are relevant to non-adiabatic transitions, conical intersections and Berry phases. Specifically, for an avoided crossing employed in the evaporative cooling of OH, we compare our exact results to those derived earlier from perturbation theory., 5 figures, to be published in Eur. Phys. J. D

The OH molecule is currently of great interest from the perspective of ultracold chemistry, quantum fluids, precision measurement and quantum computation. Crucial to these applications are the slowing, guiding, confinement and state control of OH, using electric and magnetic fields. In this article, we show that the corresponding eight-dimensional effective ground state Stark-Zeeman Hamiltonian is exactly solvable and explicitly identify the underlying chiral symmetry. Our analytical solution opens the way to insightful characterization of the magnetoelectrostatic manipulation of ground state OH. Based on our results, we also discuss a possible application to the quantum simulation of an imbalanced Ising magnet., Final version with 1 figure and an explicit discussion of the underlying symmetry. Published as PRA 88, 012503 (2013)

We propose to use an acoustic surface wave as a memory for a photon carrying orbital angular momentum. We clarify the physical mechanism that enables the transfer of information, derive the angular momentum selection rule that must be obeyed in the process, and show how to optimize the optoacoustic coupling. We theoretically demonstrate that high fidelities can be achieved, using realistic parameters, for the transfer of a coherent optical Laguerre-Gaussian state, associated with large angular momentum, to a mechanical shear mode. Our results add a significant possibility to the ongoing efforts towards the implementation of quantum information processing using photonic orbital angular momentum., Comment: 5 figures

In beginning quantum mechanics courses, symmetries of a physical system are usually introduced as operators which commute with the Hamiltonian. In this article we will consider chiral symmetries which anticommute with the Hamiltonian. Typically, introductory courses at the (under)graduate level do not discuss these simple, useful and beautiful symmetries at all. The first time a student typically encounters them is when the Dirac equation is discussed in a course on relativistic quantum mechanics, or when particle-hole symmetry is studied in the context of superconductivity. In this article, we will show how chiral symmetries can be simply elucidated using the theory of angular momentum, which is taught in virtually all introductory quantum mechanics courses.

We perform a quantum mechanical analysis of superconducting resonators subject to dielectric loss arising from charged two-level systems. We present numerical and analytical descriptions of the dynamics of energy decay from the resonator within the Jaynes-Cummings model. Our analysis allows us to distinguish the strong and weak coupling regimes of the model and to describe within each regime cases where the two-level system is unsaturated or saturated. We find that the quantum theory agrees with the classical model for weak coupling. However, for strong coupling the quantum theory predicts lower loss than the classical theory in the unsaturated regime. Also, in contrast to the classical theory, the photon number at which saturation occurs in the strong coupling quantum theory is independent of the coupling between the resonator and the two-level system., 9 pages, 8 figures

We consider a cavity optomechanical system consisting of a Bose-Einstein condensate (BEC) interacting with two counterpropagating traveling-wave modes in an optical ring cavity. In contrast to the more familiar case where the condensate is driven by the standing-wave field of a high-$Q$ Fabry-P{\'e}rot cavity we find that both symmetric and antisymmetric collective density side modes of the BEC are mechanically excited by the light field. In the semiclassical, mean-field limit where the light field and the zero-momentum mode of the condensate are treated classically the system is found to exhibit a rich multistable behavior, including the appearance of isolated branches of solutions (isolas). We also present examples of the dynamics of the system as input parameters such as the frequency of the driving lasers are varied.

We demonstrate the transfer, storage and retrieval of optical information in a spinor condensate using a two-photon Raman technique. The stored information is read out by reapplying one of the two Raman beams.

We study a hybrid optomechanical system consisting of a Bose-Einstein condensate (BEC) trapped inside a single-mode optical cavity with a moving end-mirror. The intracavity light field has a dual role: it excites a momentum side-mode of the condensate, and acts as a nonlinear spring that couples the vibrating mirror to that collective density excitation. We present the dynamics in a regime where the intracavity optical field, the mirror, and the side-mode excitation all display bistable behavior. In this regime we find that the dynamics of the system exhibits Hamiltonian chaos for appropriate initial conditions., Comment: 5 figures

We investigate the coupling of a nanomechanical oscillator in the quantum regime with molecular (electric) dipoles. We find theoretically that the cantilever can produce single-mode squeezing of the center-of-mass motion of an isolated trapped molecule and two-mode squeezing of the phonons of an array of molecules. This work opens up the possibility of manipulating dipolar crystals, which have been recently proposed as quantum memory, and more generally, is indicative of the promise of nanoscale cantilevers for the quantum detection and control of atomic and molecular systems., 3 figures, 4pages

We investigate theoretically the extension of cavity optomechanics to multiple membrane systems. We describe such a system in terms of the coupling of the collective normal modes of the membrane array to the light fields. We show these modes can be optically addressed individually and be cooled, trapped and characterized, e.g. via quantum nondemolition measurements. Analogies between this system and a linear chain of trapped ions or dipolar molecules imply the possibility of related applications in the quantum regime., Comment: 4 pages, 2 figures

The ability to control matter on the nanometer scale is greatly influenced by the van der Waals vdW interaction. Therefore, understanding and manipulating the vdW interaction is of interest to the fields of nanotechnology and atom optics. We show that near-resonant light can significantly modify atom-surface vdW interactions in the nonretarded regime. A theory based on quantized electromagnetic fields is used to calculate 1 the ordinary vdW interaction, 2 corrections to the ordinary vdW interaction due to thermal radiation, and 3 modifications to the ordinary vdW interaction that result from monochromatic laser radiation. Near- resonant laser light with an intensity of 5 W /cm 2 is predicted to double the vdW interaction strength for sodium atoms, and possible experiments to detect this effect are discussed. The strength of the van der Waals vdW interaction be- tween matter is usually determined by the atomic or bulk material properties of a system. Therefore, the vdW force can typically only be altered by changing the atomic constituents of the matter involved in the interaction, limiting the ability to control nanometer scale forces. This circumstance reso- nates with the point of view in which the vdW interaction can be thought of as being caused by the fluctuating dipole moment of a quantum-mechanical atom 1. These fluctuat- ing dipoles can then interact with each other, leading to the vdW force between the atoms. However, there exists an al- ternative perspective in which the origin of the vdW interac- tion is due to electromagnetic-field fluctuations in the vacuum, which in turn induce a fluctuating dipole moment in the atoms 2. This suggests that the vdW interaction can be affected by the radiation environment that the matter resides in, opening the exciting possibility of using light to control or even inhibit the vdW interaction. One way to change the radiation environment of matter is through temperature, which exposes the atoms to a thermal electromagnetic field. In principle, this should modify the vdW or Casimir-Polder interaction. Just such an effect has recently been observed for an atom and a nearby surface in the retarded regime 3, where the atom-surface distance z is much larger than the principle transition wavelength of the atom. However, thermal modifications are predicted to be negligible in the nonretarded regime 4,5, where distances are such that z. This is unfortunate since the ability to change the force between atoms and a surface would have an impact on atom chips, atom optics, and quantum reflection experiments.

We consider the dynamics of a vibrating and rotating end-mirror of an optical Fabry-P{\'erot} cavity that can sustain Laguerre-Gaussian modes. We demonstrate theoretically that since the intra-cavity field carries linear as well as angular momentum, radiation pressure can create bipartite entanglement between a vibrational and a rotational mode of the mirror. Further we show that the ratio of vibrational and rotational couplings with the radiation field can easily be adjusted experimentally, which makes the generation and detection of entanglement robust to uncertainties in the cavity manufacture. This constitutes the first proposal to demonstrate entanglement between two qualitatively different degrees of freedom of the same macroscopic object., Comment: 3 figures

We consider the radiative trapping and cooling of a partially reflecting mirror suspended inside an optical cavity, generalizing the case of a perfectly reflecting mirror previously considered [M. Bhattacharya and P. Meystre, Phys. Rev. Lett. 99, 073601 (2007)]. This configuration was recently used in an experiment to cool a nanometers-thick dielectric membrane [J. D. Thompson et al., e-print arXiv:0707.1724v2]. The self-consistent cavity field modes of this system depend strongly on the position of the middle mirror, leading to important qualitative differences in the radiation pressure effects: in one case, the situation is similar to that of a perfectly reflecting middle mirror, with only minor quantitative modifications. In addition, we also identify a range of mirror positions for which the radiation-mirror-coupling becomes purely dispersive and the back-action effects that usually lead to cooling are absent, although the mirror can still be optically trapped. The existence of these two regimes leads us to propose a bichromatic scheme that optimizes the cooling and trapping of partially reflective mirrors.

We show theoretically that it is possible to trap and cool the rotational motion of a macroscopic mirror made of a perfectly reflecting spiral phase element using orbital angular momentum transfer from a Laguerre-Gaussian optical field. This technique offers a promising route to the placement of the rotor in its quantum mechanical ground state in the presence of thermal noise. It also opens up the possibility of simultaneously cooling a vibrational mode of the same mirror. Lastly, the proposed design may serve as a sensitive torsional balance in the quantum regime., Comment: New cavity design, reworked title; to appear in Phys. Rev. Lett

We investigate the waveguiding properties of the optical interference pattern of two counter-propagating Laguerre-Gaussian beams. The number, helicity, radius, pitch, depth and frequencies of transverse confinement of the waveguides are simply related to the beam parameters. Quantitative connections to the familiar Gaussian optical lattice are made and an application to quantum transport is suggested., Accepted for publication in Optics Communications

A number of interesting phenomena occur at points where the energy levels of an atom or a molecule (anti) cross as a function of some parameter such as an external field. In a previous paper [M. Bhattacharya and C. Raman, Phys. Rev. Lett. 97, 140405 (2006)] we have outlined powerful mathematical techniques useful in identifying the parameter values at which such (avoided) crossings occur. In the accompanying article [M. Bhattacharya and C. Raman, Phys. Rev A 75, 033405 (2007)] we have developed the mathematical basis of these algebraic techniques in some detail. In this article we apply these level-crossing methods to the spectra of atoms and molecules in a magnetic field. In the case of atoms the final result is the derivation of a class of invariants of the Breit-Rabi Hamiltonian of magnetic resonance. These invariants completely describe the parametric symmetries of the Hamiltonian. In the case of molecules we present an indicator which can tell when the Born-Oppenheimer approximation breaks down without using any information about the molecular potentials other than the fact that they are real. We frame our discussion in the context of Feshbach resonances in the atom-pair $^{23}\mathrm{Na}\text{\ensuremath{-}}^{85}\mathrm{Rb}$ which are of current interest.

When the parameters of a physical system are varied, the eigenvalues of observables can undergo crossings and avoided crossings among themselves. It is relevant to be aware of such points since important physical processes often occur there. In a recent paper [M. Bhattacharya and C. Raman, Phys. Rev. Lett. 97, 140405 (2006)] we introduced a powerful algebraic solution to the problem of finding (avoided) crossings in atomic and molecular spectra. This was done via a mapping to the problem of locating the roots of a polynomial in the parameters of interest. In this article we describe our method in detail. Given a physical system that can be represented by a matrix, we show how to find a bound on the number of (avoided) crossings in its spectrum, the scaling of this bound with the size of the Hilbert space and the parametric dependencies of the Hamiltonian, the interval in which the (avoided) crossings all lie in parameter space, the number of crossings at any given parameter value, and the minimum separation between the (avoided) crossings. We also show how the crossings can reveal the symmetries of the physical system, how (avoided) crossings can always be found without solving for the eigenvalues, how they may sometimes be found even in case the Hamiltonian is not fully known, and how crossings may be visualized in a more direct way than displayed by the spectrum. In the accompanying paper [M. Bhattacharya and C. Raman, Phys. Rev. A 75, 033406 (2007)] we detail the application of these techniques to atoms and molecules.

We remind the reader that it is possible to tell if two or more eigenvalues of a matrix are equal, without calculating the eigenvalues. We then use this property to detect (avoided) crossings in the spectra of quantum Hamiltonians representable by matrices. This approach provides a pedagogical introduction to (avoided) crossings, is capable of handling realistic Hamiltonians analytically, and offers a way to visualize crossings which is sometimes superior to that provided by the spectrum. We illustrate the method using the Breit-Rabi Hamiltonian to describe the hyperfine-Zeeman structure of the ground state hydrogen atom in a uniform magnetic field., Comment: Accepted for publication in the American Journal of Physics

In many physical systems it is important to be aware of the crossings and avoided crossings which occur when eigenvalues of a physical observable are varied using an external parameter. We have discovered a powerful algebraic method of finding such crossings via a mapping to the problem of locating the roots of a polynomial in that parameter. We demonstrate our method on atoms and molecules in a magnetic field, where it has implications in the search for Feshbach resonances. In the atomic case our method allows us to point out a new class of invariants of the Breit-Rabi Hamiltonian of magnetic resonance. In the case of molecules, it enables us to find curve crossings with practically no knowledge of the corresponding Born-Oppenheimer potentials., 4 pages, new title, no figures, accepted by Phys. Rev. Lett

We describe a new experimental approach to probabilistic atom-photon (signal) entanglement. Two qubit states are encoded as orthogonal collective spin excitations of an unpolarized atomic ensemble. After a programmable delay, the atomic excitation is converted into a photon (idler). Polarization states of both the signal and the idler are recorded and are found to be in violation of the Bell inequality. Atomic coherence times exceeding several microseconds are achieved by switching off all the trapping fields - including the quadrupole magnetic field of the magneto-optical trap - and zeroing out the residual ambient magnetic field., Phys. Rev. Lett., in press (submitted April 29, 2005), 4 pages, 3 figures