We report the experimental demonstration of a quantum memory for collective atomic states in a far-detuned optical dipole trap. Generation of the collective atomic state is heralded by the detection of a Raman scattered photon and accompanied by storage in the ensemble of atoms. The optical dipole trap provides confinement for the atoms during the quantum storage while retaining the atomic coherence. We probe the quantum storage by cross-correlation of the photon pair arising from the Raman scattering and the retrieval of the atomic state stored in the memory. Non-classical correlations are observed for storage times up to 60 microseconds.
We demonstrate electromagnetically induced transparency (EIT) in a sample of rubidium atoms, trapped in an optical dipole trap. Mixing a small amount of $σ^-$-polarized light to the weak $σ^+$-polarized probe pulses, we are able to measure the absorptive and dispersive properties of the atomic medium at the same time. Features as small as 4 kHz have been detected on an absorption line with 20 MHz line width.
The radiation pressure of two detuned laser beams can create a stable trap for a suspended cavity mirror; here it is shown that such a configuration entangles the output light fields via interaction with the mirror. Intra-cavity, the opto-mechanical system can become entangled also. The degree of entanglement is quantified spectrally using the logarithmic negativity. Entanglement survives in the experimentally accessible regime of gram-scale masses subject to thermal noise at room temperature.
We have studied a general technique for laser cooling a cloud of polarized trapped atoms down to the Doppler temperature. A one-dimensional optical molasses using polarized light cools the axial motional degree of freedom of the atoms in the trap. Cooling of the radial degrees of freedom can be modelled by reabsorption of scattered photons in the optically dense cloud. We present experimental results for a cloud of chromium atoms in a magnetic trap. A simple model based on rate equations shows quantitative agreement with the experimental results. This scheme allows us to readily prepare a dens…
We study entanglement of the motional degrees of freedom of two tethered and optically trapped microdisks inside a single cavity. By properly choosing the position of the trapped objects in the optical cavity and driving proper modes of the cavity it is possible to equip the system with linear and quadratic optomechanical couplings. We show that a parametric coupling between the fundamental vibrational modes of two tethered mircodiscs can be generated via a time modulated input laser. For a proper choice of the modulation frequency, this mechanism can drive the motion of the microdisks into an…
We present a detailed analysis and design of a neutral atom quantum logic device based on atoms in optical traps interacting via dipole-dipole coupling of Rydberg states. The dominant physical mechanisms leading to decoherence and loss of fidelity are enumerated. Our results support the feasibility of performing single and two-qubit gates at MHz rates with decoherence probability and fidelity errors at the level of $10^{-3}$ for each operation. Current limitations and possible approaches to further improvement of the device are discussed.
We systematically investigate the bistable behavior and squeezing property of the librational mode of a levitated nonspherical nanoparticle trapped by laser beams. By expanding the librational potential to the forth order of the librational angle $θ$, we find that the nonlinear coefficient of this mode is dependent only on the size and material of nanoparticle, but independent of trapping potential shape. The bistability and hysteresis are displayed when the driving frequency is red-detuned to the librational mode. In the blue-detuned region, we have studied squeezing of the variance of librat…
A tapered optical nanofiber simultaneously used to trap and optically interface of cold atoms through evanescent fields constitutes a new and well controllable hybrid quantum system. The atoms are trapped in two parallel 1D optical lattices generated by suitable far blue and red detuned evanescent field modes very close to opposite sides of the nanofiber surface. Collective electronic excitations (excitons) of each of the optical lattices are resonantly coupled to the second lattice forming symmetric and antisymmetric common excitons. In contrast to the inverse cube dependence of the individua…
We systematically investigate the multi-stability behaviour and cooling of both librational and translational modes of an optically levitated nonspherical nanoparticle. By expanding the trapping potential to the fourth order of both the translational and librational freedom degrees, we deduce the nonlinearity of them and their nonlinear coupling. Through stability analysis, we find that the system presents multi-stability when either the librational or the translational drive is red-detuned. The system will be stabilized if and only if these two drives are both blue-detuned. In the steady stat…
The quantum walk is the quantum analogue of the well-known random walk, which forms the basis for models and applications in many realms of science. Its properties are markedly different from the classical counterpart and might lead to extensive applications in quantum information science. In our experiment, we implemented a quantum walk on the line with single neutral atoms by deterministically delocalizing them over the sites of a one-dimensional spin-dependent optical lattice. With the use of site-resolved fluorescence imaging, the final wave function is characterized by local quantum state…
We experimentally investigate the coherence properties of a qubit stored in the Zeeman substates of the 5S1/2, F=1 hyperfine ground level of a single optically trapped Rb-87 atom. Larmor precession of a single atomic spin-1 system is observed by preparing the atom in a defined initial spin-state and then measuring the resulting state after a programmable period of free evolution. Additionally, by performing quantum state tomography, maximum knowledge about the spin coherence is gathered. By using an active magnetic field stabilization and without application of a magnetic guiding field we achi…
Recent developments in space technology like micro-propulsion systems for drag-free control, thermal shielding, ultra-stable laser sources and stable optical cavities set an ideal platform for quantum optomechanical experiments with optically trapped dielectric spheres. Here, we will provide an overview of the results of recent studies aiming at the realization of the space mission MAQRO to test the foundations of quantum physics in a parameter regime orders of magnitude beyond existing experiments. In particular, we will discuss DECIDE, which is an experiment to prepare and then study a Schrö…
The fidelity of the gate operation and the coherence time of neutral atoms trapped in an optical dipole trap are figures of merit for the applications. The motion of the trapped atom is one of the key factors which influence the gate fidelity and coherence time. The motion has been considered as a classical oscillator in analyzing the influence. Here we treat the motion of the atom as a quantum oscillator. The population on the vibrational states of the atom are considered in analyzing the gate fidelity and decoherence. We show that the fidelity of a coherent rotation gate is dramatically limi…
Ultra-cold atoms trapped in an optical dipole trap and prepared in a coherent superposition of their hyperfine ground states, decohere as they interact with their environment. We demonstrate than the loss in coherence in an "echo" experiment, which is caused by mechanisms such as Rayleigh scattering, can be suppressed by the use of a new pulse sequence. We also show that the coherence time is then limited by mixing to other vibrational levels in the trap and by the finite lifetime of the internal quantum states of the atoms.
We use microwave induced adiabatic passages for selective spin flips within a string of optically trapped individual neutral Cs atoms. We position-dependently shift the atomic transition frequency with a magnetic field gradient. To flip the spin of a selected atom, we optically measure its position and sweep the microwave frequency across its respective resonance frequency. We analyze the addressing resolution and the experimental robustness of this scheme. Furthermore, we show that adiabatic spin flips can also be induced with a fixed microwave frequency by deterministically transporting the …
We investigate the emission of single photons from CdSe/CdS dot-in-rods which are optically trapped in the focus of a deep parabolic mirror. Thanks to this mirror, we are able to image almost the full 4$π$ emission pattern of nanometer-sized elementary dipoles and verify the alignment of the rods within the optical trap. From the motional dynamics of the emitters in the trap we infer that the single-photon emission occurs from clusters comprising several emitters. We demonstrate the optical trapping of rod-shaped quantum emitters in a configuration suitable for efficiently coupling an ensemble…
We perform spectroscopy on the hyperfine splitting of $^{85}$Rb atoms trapped in far-off-resonance optical traps. The existence of a spatially dependent shift in the energy levels is shown to induce an inherent dephasing effect, which causes a broadening of the spectroscopic line and hence an inhomogeneous loss of atomic coherence at a much faster rate than the homogeneous one caused by spontaneous photon scattering. We present here a number of approaches for reducing this inhomogeneous broadening, based on trap geometry, additional laser fields, and novel microwave pulse sequences. We then sh…
We report the finding of "triply magic" conditions (the doubly magic frequency-intensity conditions of an optical dipole trap plus the magic magnetic field) for the microwave transitions of optically trapped alkali-metal atoms. The differential light shift (DLS) induced by a degenerate two-photon process is adopted to compensate a DLS associated with the one-photon process. Thus, doubly magic conditions for the intensity and frequency of the optical trap beam can be found. Moreover, the DLS decouples from the magnetic field in a linearly polarized optical dipole trap, so that the magic conditi…
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 correspond…
Atomic ensembles have many potential applications in quantum information science. Owing to collective enhancement, working with ensembles at high densities increases the overall efficiency of quantum operations, but at the same time also increases the collision rate and leads to faster decoherence. Here we report on experiments with optically trapped 87Rb atoms demonstrating a 20-fold increase of the coherence time when a dynamical decoupling sequence with more than 200 pi-pulses is applied. We perform quantum process tomography and demonstrate that using the decoupling scheme a dense ensemble…
Optical trapping of molecules with long coherence times is crucial for many protocols in quantum information and metrology. However, the factors that limit the lifetimes of the trapped molecules remain elusive and require improved understanding of the underlying molecular structure. Here we show that measurements of vibronic line strengths in weakly and deeply bound $^{88}$Sr$_2$ molecules, combined with \textit{ab initio} calculations, allow for unambiguous identification of vibrational quantum numbers. This, in turn, enables the construction of refined excited potential energy curves that in…
Cold inelastic collisions between confined cesium (Cs) atoms and Cs$\_2$ molecules are investigated inside a CO$\_2$ laser dipole trap. Inelastic atom-molecule collisions can be observed and measured with a rate coefficient of $\sim 2.5 \times 10^{-11} $cm$^3$ s$^{-1}$, mainly independent of the molecular ro-vibrational state populated. Lifetimes of purely atomic and molecular samples are essentially limited by rest gas collisions. The pure molecular trap lifetime ranges 0,3-1 s, four times smaller than the atomic one, as is also observed in a pure magnetic trap. We give an estimation of the i…
Laser-cooled atoms coupled to nanophotonic structures constitute a powerful research platform for the exploration of new regimes of light-matter interaction. While the initialization of the atomic internal degrees of freedom in these systems has been achieved, a full preparation of the atomic quantum state also requires controlling the center of mass motion of the atoms at the quantum level. Obtaining such control is not straightforward, due to the close vicinity of the atoms to the photonic system that is at ambient temperature. Here, we demonstrate cooling of individual neutral Cesium atoms,…
We demonstrate size selective optical trapping and transport for nanoparticles near an optical nanofiber taper. Using a two-wavelength, counter-propagating mode configuration, we show that 100 nm diameter and 150 nm diameter gold nanospheres (GNSs) are trapped by the evanescent field in the taper region at different optical powers. Conversely, when one nanoparticle species is trapped the other may be transported, leading to a sieve-like effect. Our results show that sophisticated optical manipulation can be achieved in a passive configuration by taking advantage of mode behavior in nanophotoni…
Collective coherent scattering of laser light induces strong light forces between polarizable point particles. These dipole forces are strongly enhanced in magnitude and distance within the field of an optical waveguide so that at low temperature the particles self-order in strongly bound regular patterns. The stationary configurations typically exhibit super-radiant scattering with strong particle and light confinement. Here we study collective excitations of such self-consistent crystalline particle-light structures as function of particle number and pump strength. Multiple scattering and ab…
This is a chapter of a recently published book entitled Atom Chips, edited by Jakob Reichel and Vladan Vuletic. The contents of this chapter include: Basic Principles; Atomic-Fountain versus Trapped-Atom Clocks; Optical-Transition Clocks versus Microwave Clocks; Clocks with Magnetically Trapped Atoms--Fundamental Limits and Experimental Demonstrations; Readout in Trapped-Atom Clocks; and Spin Squeezing.
We review recent works on optomechanics of optically trapped microspheres and nanoparticles in vacuum, which provide an ideal system for studying macroscopic quantum mechanics and ultrasensitive force detection. An optically trapped particle in vacuum has an ultrahigh mechanical quality factor as it is well-isolated from the thermal environment. Its oscillation frequency can be tuned in real time by changing the power of the trapping laser. Furthermore, an optically trapped particle in vacuum may rotate freely, a unique property that does not exist in clamped mechanical oscillators. In this re…
Optically trapped ensembles are of crucial importance for frequency measurements and quantum memories, but generally suffer from strong dephasing due to inhomogeneous density and light shifts. We demonstrate a drastic increase of the coherence time to 21 s on the magnetic field insensitive clock transition of Rb-87 by applying the recently discovered spin self-rephasing. This result confirms the general nature of this new mechanism and thus shows its applicability in atom clocks and quantum memories. A systematic investigation of all relevant frequency shifts and noise contributions yields a s…
We propose a scheme to implement the quantum teleportation protocol with single atoms trapped in cavities. The scheme is based on the adiabatic passage and the polarization measurement. We show that it is possible to teleport the internal state of an atom trapped in a cavity to an atom trapped in another cavity with the success probability of 1/2 and the fidelity of 1. The scheme is resistant to a number of considerable imperfections such as the violation of the Lamb-Dicke condition, weak atom-cavity coupling, spontaneous emission, and detection inefficiency.
We propose a scheme for preparing an EPR state in position and momentum of a pair of distantly-separated trapped atoms. The scheme utilizes the entangled light fields output from a nondegenerate optical parametric amplifier. Quantum state exchange between these fields and the motional states of the trapped atoms is accomplished via interactions in cavity QED.
We demonstrate an integrated magnetic ``atom chip'' which transports cold trapped atoms near a surface with very high positioning accuracy. Time-dependent currents in a lithographic conductor pattern create a moving chain of magnetic potential wells; atoms are transported in these wells while remaining confined in all three dimensions. We achieve fluxes up to 10^6 /s with a negligible heating rate. An extension of this ``atomic conveyor belt'' allows the merging of magnetically trapped atom clouds by unification of two Ioffe-Pritchard potentials. Under suitable conditions, the clouds merge wit…
We study semi-classical slow light propagation in trapped two level atomic quantum gases. The temperature dependent behaviors of both group velocity and transmissions are compared for low temperature Bose, Fermi, and Boltzman gases within the local density approximation for their spatial density profile.
Entanglement lies at the heart of quantum mechanics and in recent years has been identified as an essential resource for quantum information processing and computation. Creating highly entangled multi-particle states is therefore one of the most challenging goals of modern experimental quantum mechanics, touching fundamental questions as well as practical applications. Here we report on the experimental realization of controlled collisions between individual neighbouring neutral atoms trapped in the periodic potential of an optical lattice. These controlled interactions act as an array of quan…
We sympathetically cool a trapped 112Cd+ ion by directly Doppler-cooling a 114Cd+ ion in the same trap. This is the first demonstration of optically addressing a single trapped ion being sympathetically cooled by a different species ion. Notably, the experiment uses a single laser source, and does not require strong focusing. This paves the way toward reducing decoherence in an ion trap quantum computer based on Cd+ isotopes.
We propose a search for low mass dark matter particles through momentum recoils caused by their scattering from trapped, nm-scale objects. Our projections show that even with a modest array of fg-mass sensors, parameter-space beyond the reach of existing experiments can be explored. The case of smaller, ag-mass sensors is also analyzed - where dark matter can coherently scatter from the entire sensor - enabling a large enhancement in the scattering cross-section relative to interactions with single nuclei. Large arrays of such sensors have the potential to explore new parameter space down to d…
Quantum thermodynamics of a trapped two-level atom under the influence of a controlled light field is investigated. The population dynamics and decoherency function are obtained and discussed. The characteristic functions, work distribution functions and Helmholtz free energies are calculated and the consistency with the Jarzynski theorem is verified.
We investigate the quantized states of a two-level Rb atom which is trapped by the optical dipole potential when the atom interacts with a helical optical tube (HOT) light field. The analysis shows that the stationary states can be defined by a triplet of quantum numbers and the corresponding wavefunctions exhibit a twisted, spiral-like 3D spatial shape.
Trapped, laser-cooled rubidium atoms are transferred between two strongly focused, horizontal, orthogonally intersecting laser beams. The transfer efficiency is studied as a function of the vertical distance between the beam axes. Optimum transfer is found when the distance equals the beam waist radius. Numerical simulations reproduce well the experimental results.
Dimensionality serves as an indispensable ingredient in any attempt to formulate the low-dimensional physics, and studying the dimensional crossover at a fundamental level is challenging. The purpose of this work is to study the hierarchical dimensional crossovers, namely the crossover from three dimensions (3D) to quasi-2D and then to 1D. Our system consists of a 3D Bose-Einstein condensate (BEC) trapped in an anisotropic 2D optical lattice characterized by the lattice depths $V_1$ along the $x$ direction and $V_2$ along the $y$ direction, respectively, where the hierarchical dimensional cros…
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.
An experiment is performed where a single rubidium atom trapped within a high-finesse optical cavity emits two independently triggered entangled photons. The entanglement is mediated by the atom and is characterized both by a Bell inequality violation of S=2.5, as well as full quantum-state tomography, resulting in a fidelity exceeding F=90%. The combination of cavity-QED and trapped atom techniques makes our protocol inherently deterministic - an essential step for the generation of scalable entanglement between the nodes of a distributed quantum network.
The transmission spectrum for one atom strongly coupled to the field of a high-finesse optical resonator is observed to exhibit a clearly resolved vacuum-Rabi splitting characteristic of the normal modes in the eigenvalue spectrum of the atom-cavity system. A new Raman scheme for cooling atomic motion along the cavity axis enables a complete spectrum to be recorded for an individual atom trapped within the cavity mode, in contrast to all previous measurements in cavity QED that have required averaging over many atoms.
We describe a scheme for producing conditional nonlinear phase shifts on two-photon optical fields using an interaction with one or more ancilla two-level atomic systems. The conditional field state transformations are induced by using high efficiency fluorescence shelving measurements on the atomic ancilla. The scheme can be nearly deterministic and is of obvious benefit for quantum information applications.
We collect the fluorescence from two trapped atomic ions, and measure quantum interference between photons emitted from the ions. The interference of two photons is a crucial component of schemes to entangle atomic qubits based on a photonic coupling. The ability to preserve the generated entanglement and to repeat the experiment with the same ions is necessary to implement entangling quantum gates between atomic qubits, and allows the implementation of protocols to efficiently scale to larger numbers of atomic qubits.
We propose a scheme for conditional implementation of a quantum phase gate by using distant atoms trapped in different optical cavities. Instead of direct interaction between atoms, the present scheme makes use of quantum interference of polarized photons decaying from the optical cavities to conditionally create the desired quantum phase gate between two distant atoms. The proposed scheme only needs linear optical elements and a two-fold coincidence detection, and are insensitive to the quantum noise. The scheme can be directly used to prepare any quantum state of many distant atoms.
We explore how to cool atomic collective excitations in an optically-driven three-level atomic ensemble, which may be described by a model of coupled two harmonic oscillators (HOs) with a time-dependent coupling. Moreover, the coupled two-HO model is further generalized to address other cooling issues, where the lower-frequency HO can be cooled whenever the cooling process dominates over the heating one during the sideband transitions. Unusually, due to the absence of the heating process, the optimal cooling of our first cooling protocol for collective excitations in an atomic ensemble could b…
In a cold atom gas subject to a 2D spin-dependent optical lattice potential with hexagonal symmetry, trapped atoms undergo orbital motion around the potential minima. Such atoms are elementary quantum rotors. We develop the theory of such quantum rotors. Wave functions, energies, and degeneracies are determined for both bosonic and fermionic atoms, and magnetic dipole transitions between the states are elucidated. Quantum rotors in optical lattices with precisely one atom per unit cell can be used as high precision rotation sensors, accelerometers, and magnetometers.
Stochastic cooling of trapped atoms is considered for a laser-beam configuration with beam waists equal or smaller than the extent of the atomic cloud. It is shown, that various effects appear due to this transverse confinement, among them heating of transverse kinetic energy. Analytical results of the cooling in dependence on size and location of the laser beam are presented for the case of a non-degenerate vapour.
A cooling scheme for trapped atoms is proposed, which combines cavity-enhanced scattering and electromagnetically induced transparency. The cooling dynamics exploits a three-photon resonance, which combines laser and cavity excitations. It is shown that relatively fast ground-state cooling can be achieved in the Lamb-Dicke regime and for large cooperativity. Efficient ground-state cooling is found for parameters of ongoing experiments.
We consider the propagation of a quantized polarized light in a magneto-optically manipulated atomic ensemble with a tripod configuration. Polariton formalism is applied when the medium is subjected to a washboard magnetic field under electromagnetically induced transparency. The dark-state polariton with multiple components is achieved. We analyze quantum dynamics of the dark-state polariton by some experiment data from rubidium D1-line. It is found that one component propagates freely, however the wavepacket trajectory of the other component performs Bloch oscillations.
We theoretically analyze the cooling dynamics of an atom which is tightly trapped inside a high-finesse optical resonator. Cooling is achieved by suitably tailored scattering processes, in which the atomic dipole transition either scatters a cavity photon into the electromagnetic field external to the resonator, or performs a stimulated emission into the cavity mode, which then dissipates via the cavity mirrors. We identify the parameter regimes in which the atom center-of-mass motion can be cooled into the ground state of the external trap. We predict, in particular, that for high cooperativi…
Generalized single-atom Maxwell-Bloch equations for optically dense media are derived taking into account non-cooperative radiative atom-atom interactions. Applying a Gaussian approximation and formally eliminating the degrees of freedom of the quantized radiation field and of all but a probe atom leads to an effective time-evolution operator for the probe atom. The mean coherent amplitude of the local field seen by the atom is shown to be given by the classical Lorentz-Lorenz relation. The second-order correlations of the field lead to terms that describe relaxation or pump processes and leve…
