Various parameters of a trapped collection of cold and ultracold atoms can be determined non--destructively by measuring the phase shift of an off--resonant probe beam, caused by the state dependent index of refraction of the atoms. The dispersive light--atom interaction, however, gives rise to a differential light shift (AC Stark shift) between the atomic states which, for a nonuniform probe intensity distribution, causes an inhomogeneous dephasing between the atoms. In this paper, we investigate the effects of this inhomogeneous light shift in non--destructive measurement schemes. We interpret our experimental data on dispersively probed Rabi oscillations and Ramsey fringes in terms of a simple light shift model which is shown to describe the observed behavior well. Furthermore, we show that by using spin echo techniques, the inhomogeneous phase shift distribution between the two clock levels can be reversed.
Non-destructive detection of photonic qubits will enable important applications in photonic quantum information processing and quantum communications. Here, we present an approach based on a solid-state cavity containing an ensemble of rare-earth ions. First a probe pulse containing many photons is stored in the ensemble. Then a single signal photon, which represents a time-bin qubit, imprints a phase on the ensemble that is due to the AC Stark effect. This phase does not depend on the exact timing of the signal photon, which makes the detection insensitive to the time-bin qubit state. Then th…
A method for non-destructive characterization of a dipole trapped atomic sample is presented. It relies on a measurement of the phase-shift imposed by cold atoms on an optical pulse that propagates through a free space Mach-Zehnder interferometer. Using this technique we are able to determine, with very good accuracy, relevant trap parameters such as the atomic sample temperature, trap oscillation frequencies and loss rates. Another important feature is that our method is faster than conventional absorption or fluorescence techniques, allowing the combination of high-dynamical range measuremen…
We investigate the dynamics for a two level atomic system entangled to coherent states using the recently developed mode invisibility technique. Using a quantum 2-level probe, we demonstrate a way to non-destructively measure a number of properties between a qubit entangled with a generalized CAT state, including the amplitude of the coherent state, the location and relative excitation of the qubit, and the von Neumann entropy. Our results indicate a connection between this last quantity and the interferometric phase shift of the probe, thereby suggesting a possible way to experimentally measu…
We present a semi-classical theory for light deflection by a coherent $Λ$-type three-level atomic medium in an inhomogeneous magnetic field or an inhomogeneous control laser. When the atomic energy levels (or the Rabi coupling by the control laser) are position-dependent due to the Zeeman effect by the inhomogeneous magnetic field (or the inhomogeneity of the control field profile), the spatial dependence of the refraction index of the atomic medium will result in an observable deflection of slow signal light when the electromagnetically induced transparency happens to avoid medium absorption.…
We describe an easily implementable method for non-destructive measurements of ultracold atomic clouds based on dark field imaging of spatially resolved Faraday rotation. The signal-to-noise ratio is analyzed theoretically and, in the absence of experimental imperfections, the sensitivity limit is found to be identical to other conventional dispersive imaging techniques. The dependence on laser detuning, atomic density and temperature is characterized in a detailed comparison with theory. Due to low destructiveness, spatially resolved images of the same cloud can be acquired up to 2000 times. …
In a recent paper [Gorshkov et al., Phys. Rev. Lett. 98, 123601 (2007)] and in the two preceding papers [Gorshkov et al., Phys. Rev. A 76, 033804 (2007); 76, 033805 (2007)], we used a universal physical picture to optimize and demonstrate equivalence between a wide range of techniques for storage and retrieval of photon wave packets in homogeneously broadened Lambda-type atomic media, including the adiabatic reduction of the photon group velocity, pulse-propagation control via off-resonant Raman techniques, and photon-echo-based techniques. In the present paper, we generalize this treatment to…
We investigate the decoherence of a superposition of symmetric collective internal states of an atomic ensemble due to inhomogeneous coupling to external control fields. For asymptotically large system, we find the characteristic decoherence rate scales as $\sqrt{N}$ with $N$ being the total number of atoms. Our results shed new light on attempts for quantum information processing and storage with atomic ensembles.
We report on non-destructive observation of Rabi oscillations on the Cs clock transition. The internal atomic state evolution of a dipole-trapped ensemble of cold atoms is inferred from the phase shift of a probe laser beam as measured using a Mach-Zehnder interferometer. We describe a single color as well as a two-color probing scheme. Using the latter, measurements of the collective pseudo-spin projection of atoms in a superposition of the clock states are performed and the observed spin fluctuations are shown to be close to the standard quantum limit.
We present a technique for atomic density measurements by the off-resonant phase-shift induced on a two-frequency, coherently-synthesised light beam. We have used this scheme to measure the column density of a magnetically trapped atom cloud and to monitor oscillations of the cloud in real time by making over a hundred non-destructive local density measurments. For measurements using pulses of 10,000-100,000 photons lasting ~10 microsecond, the precision is limited by statistics of the photons and the photodiode avalanche. We explore the relationship between measurement precision and the unwan…
The effect of inhomogeneous coupling between three-level atoms and external light fields is studied in the electromagnetically induced transparency (EIT) quantum memory techqnique. By introducing a subensemble-atomic system to deal with present inhomogeneous coupling case, we find there is a non-symmetric dark-state subspace (DSS) that allows the EIT quantum memory technique to function perfectly. This shows that such memory scheme can work ideally even if the atomic state is very far from being a symmetric one.
We demonstrate active control of inhomogeneous dephasing and rephasing for single collective atomic spin excitations (spin-waves) created by spontaneous Raman scattering in a quantum memory based on cold $^{87}$Rb atoms. The control is provided by a reversible external magnetic field gradient inducing an inhomogeneous broadening of the atomic hyperfine levels. We demonstrate experimentally that active rephasing preserves the single photon nature of the retrieved photons. Finally, we show that the control of the inhomogeneous dephasing enables the creation of time-separated spin-waves in a sing…
The evanescent field outside an optical nanofiber (ONF) can create optical traps for neutral atoms. We present a non-destructive method to characterize such trapping potentials. An off-resonance linearly polarized probe beam that propagates through the ONF experiences a slow axis of polarization produced by trapped atoms on opposite sides along the ONF. The transverse atomic motion is imprinted onto the probe polarization through the changing atomic index of of refraction. By applying a transient impulse, we measure a time-dependent polarization rotation of the probe beam that provides both a …
We describe a theoretical scheme that allows for transfer of quantum states of atomic collective excitation between two macroscopic atomic ensembles localized in two spatially-separated domains. The conception is based on the occurrence of double-exciton dark states due to the collective destructive quantum interference of the emissions from the two atomic ensembles. With an adiabatically coherence manipulation for the atom-field couplings by stimulated Ramann scattering, the dark states will extrapolate from an exciton state of an ensemble to that of another. This realizes the transport of qu…
A new scheme of photon echo based quantum memory in the optimal optical QED cavity with off-resonant Raman atomic transition is proposed. The scheme employs the atomic ensembles characterized by an optically thin resonant transition and natural inhomogeneous broadening of the resonant line composed of the arbitrary narrow homogeneous spectral components. The scheme provides robust and quite simple coherent control of the light-atoms dynamics that can be implemented by using an existing optical technique and opens a practical way for realization of the efficient long-lived multi-mode optical qu…
We propose a hybrid quantum-classical atomic clock protocol where the interrogation of an ensemble of uncorrelated atoms in a spin-coherent state is used to feedback one (or more) spin-squeezed atomic ensembles toward their optimal phase sensitivity point. This protocol overcomes the stability of a single Ramsey clock and it reaches a Heisenberg-limited stability while avoiding non-destructive measurements. Analytical predictions are compared with numerical simulations of clocks operations including correlated 1/f local oscillator noise.
Theoretical studies of superradiant lasing on optical clock transitions predict a superb frequency accuracy and precision closely tied to the bare atomic linewidth. Such a superradiant laser is also robust against cavity fluctuations when the spectral width of the lasing mode is much larger than that of the atomic medium. Recent predictions suggest that this unique feature persists even for a hot and thus strongly broadened ensemble, provided the effective atom number is large enough. Here we use a second-order cumulant expansion approach to study the power, linewidth and lineshifts of such a …
We present the experimental demonstration of non-destructive probing of the 1S0-3P0 clock transition probability in an optical lattice clock with 87Sr atoms. It is based on the phase shift induced by the atoms on a weak off-resonant laser beam. The method we propose is a differential measurement of this phase shift on two modulation sidebands with opposite detuning with respect to the 1S0-1P1 transition, allowing a detection limited by the photon shot noise. We have measured an atomic population of 10^4 atoms with a signal to noise ratio of 100 per cycle, while keeping more than 95% of the ato…
Theoretical prediction of antilocalization of light in ultracold atomic gas samples, in the weak localization regime, is reported. Calculations and Monte-Carlo simulations show that, for selected spectral ranges in the vicinity of atomic 85Rb hyperfine transitions, quantum coherence in optical transitions through nondegenerate hyperfine levels in multiple light scattering generates destructive interference in otherwise reciprocal scattering paths. This effect leads to enhancement factors less than unity in a coherent backscattering geometry, and suggests the possibility of enhanced diffusion o…
We determine the ground state properties of inhomogeneous mixtures of bosons and fermions in cubic lattices by studying the Bose-Fermi Hubbard model including parabolic confining potentials. We present the exact solution in the limit of vanishing hopping (ultradeep lattices) and study the resulting domain structure of composite particles. For finite hopping we determine the domain boundaries between Mott-insulator plateaux and hopping-dominated regions for lattices of arbitrary dimensionality within perturbation theory. The results are compared with a new numerical method that is based on a Gu…
We report on a novel experiment to generate non-classical atomic states via quantum non-demolition (QND) measurements on cold atomic samples prepared in a high finesse ring cavity. The heterodyne technique developed for the QND detection exhibits an optical shot-noise limited behavior for local oscillator optical power of a few hundred \muW, and a detection bandwidth of several GHz. This detection tool is used in single pass to follow non destructively the internal state evolution of an atomic sample when subjected to Rabi oscillations or a spin-echo interferometric sequence.
We propose a new method for efficient storage and recall of non-stationary light fields, e.g. single photon time-bin qubits, in optically dense atomic ensembles. Our approach to quantum memory is based on controlled, reversible, inhomogeneous broadening. We briefly discuss experimental realizations of our proposal.
In this paper we present a state vector analysis of the generation of atomic spin squeezing by measurement of an optical phase shift. The frequency resolution is improved when a spin squeezed sample is used for spectroscopy in place of an uncorrelated sample. When light is transmitted through an atomic sample some photons will be scattered out of the incident beam, and this has a destructive effect on the squeezing. We present quantitative studies for three limiting cases: the case of a sample of atoms of size smaller than the optical wavelength, the case of a large dilute sample and the case …
In this work we study the properties of the atomic entanglement in the eigenstates spectrum of the inhomogeneous Tavis-Cummings Model. The inhomogeneity is present in the coupling among the atoms with quantum electromagnetic field. We calculate analytical expressions for the concurrence and we found that this exhibits a strong dependence on the inhomogeneity.
We show that, under certain circumstances, an optical field in a two-mode squeezed vacuum (TMSV) state can propagate through a lossy atomic medium without degradation or evolution. Moreover, the losses give rise to that state when a different state is initially injected into the medium. Such a situation emerges in a Λ-type atomic system, in which both optical transitions are driven by strong laser fields that are two-photon resonant with the respective signal modes. Then the interactions of the two signal modes with the ground-state atomic coherence interfere destructively, thereby ensuring th…
We consider light trapping in an amplifying medium consisting of cold alkali-metal atoms; the atomic gas plays a dual role as a scattering and as a gain medium. We perform Monte-Carlo simulations for the combined processes. In some configurations of the inhomogeneous distribution this leads to a point of instability behavior and a signature of random lasing in a cold atomic gas.
Spontaneous Raman emission in atomic gases provides an attractive source of photon pairs with a controllable delay. We show how this technique can be implemented in solid state systems by appropriately shaping the inhomogeneous broadening. Our proposal is eminently feasible with current technology and provides a realistic solution to entangle remote rare-earth doped solids in a heralded way.
We present a technique, based on atoms coupled to an optical cavity, for non-destructive detection of trapped ions. We demonstrate the vacuum-Rabi splitting (VRS), arising due to the collective strong coupling of ultracold Rb atoms to a cavity, to change in presence of trapped Rb+ ions. The Rb+ ions are optically dark and the Rb atoms are prepared in a dark magneto-optical trap (MOT). The VRS is measured on an optically open transition of the initially dark Rb atoms. The measurement itself is fast, non-destructive and has sufficient fidelity to permit the measurement of atomic-state selective …
Atomic population transfer in an inhomogeneously broadened optical medium is analyzed for on-demand photon storage-time control in both atomic frequency comb (AFC) and phase locked echoes. In AFC the photon storage mechanism belongs to the conventional three-pulse photon echoes, while the storage time control is limited by conventional two-pulse photon echoes.
A scheme for coherent manipulation of collective atomic states is developed such that total subradiant states, in which spontaneous emission is suppressed into all directions due to destructive interference between neighbor atoms, can be created in an extended atomic ensemble. The optimal conditions for creation of such states and suitability of them for quantum storage are discussed. It is shown that in order to achieve the maximum signal-to-noise ratio the shape of a light pulse to be stored and reconstructed using a homogeneously broadened absorbtion line of an atomic system should be a tim…
We study theoretically and experimentally the quantification of non-Gaussian distributions via non-destructive measurements. Using the theory of cumulants, their unbiased estimators, and the uncertainties of these estimators, we describe a quantification which is simultaneously efficient, unbiased by measurement noise, and suitable for hypothesis tests, e.g., to detect non-classical states. The theory is applied to cold $^{87}$Rb spin ensembles prepared in non-gaussian states by optical pumping and measured by non-destructive Faraday rotation probing. We find an optimal use of measurement reso…
By introducing a suitable Lagrangian, a canonical quantization of the electromagnetic field in the presence of a non-dispersive bi-anisotropic inhomogeneous magnetodielectric medium is investigated. A tensor projection operator is defined and the commutation relation between the vector potential and its canonically conjugate variable is written in terms of the projection operator. The quantization method is generalized in the presence of the atomic systems. The spontaneous emission of a two-level atom located in a non-dispersive anisotropic megnetodielectric medium is studied.
Inhomogeneous mass trap for dark-state polaritons in atomic media
National Central University（中央大学）；National Tsing Hua University（清华大学）；National Center for Excellence in Quantum Information Science and Engineering, National Tsing Hua University（国家量子信息科学与工程卓越中心）；Physics Division, National Center for Theoretical Sciences（理论科学国家中心物理部）；Quantum Technology Center, National Central University（量子技术中心）
We analyze in detail the possibility to use charge-dipole interaction between a single polar molecule or a 1D molecular array and a single Rydberg atom to read out rotational populations. The change in the Rydberg electron energy is conditioned on the rotational state of the polar molecules, allowing for realization of a CNOT quantum gate between the molecules and the atom. Subsequent readout of the atomic fluorescence results in a non-destructive measurement of the rotational state. We study the interaction between a 1D array of polar molecules and an array or a cloud of atoms in a Rydberg su…
We present a detailed analysis of a quantum memory for photons based on controlled and reversible inhomogeneous broadening (CRIB). The explicit solution of the equations of motion is obtained in the weak excitation regime, making it possible to gain insight into the dependence of the memory efficiency on the optical depth, and on the width and shape of the atomic spectral distributions. We also study a simplified memory protocol which does not require any optical control fields.
When N driven atoms emit in phase into a high-Q cavity mode, the intracavity field generated by collective scattering interferes destructively with the pump driving the atoms. Hence atomic fluorescence is suppressed and cavity loss becomes the dominant decay channel for the whole ensemble. Microscopically 3D light-intensity minima are formed in the vicinity of the atoms that prevent atomic excitation and form a regular lattice. The effect gets more pronounced for large atom numbers, when the sum of the atomic decay rates exceeds the rate of cavity losses and one would expect the opposite behav…
Ensemble of identical two level atoms in dark state neither adsorbs nor emits photons due to destructive interference. It can be used for the source of energy for nano-devices. In Tavis-Cummings cavity the change of light-atom coupling cannot destroy the dark state. We propose the method of dark states preparation based on photon pumping and drain from the optical cavity with two atoms, one from which has Stark or Zeeman splitting of energy levels. This splitting is removed before photon drain from the cavity. The dark state yield after one such cycle has the order of energy level splitting. W…
An imaging system is presented that is capable of far-detuned non-destructive imaging of a Bose-Einstein condensate with the signal proportional to the second spatial derivative of the density. Whilst demonstrated with application to $^{85}\text{Rb}$, the technique generalizes to other atomic species and is shown to be capable of a signal to noise of ${\sim}25$ at $1$GHz detuning with $100$ in-trap images showing no observable heating or atom loss. The technique is also applied to the observation of individual trajectories of stochastic dynamics inaccessible to single shot imaging. Coupled wit…
We study quantum dynamics of many-qubit systems strongly coupled to a quantized electromagnetic cavity field in the presence of decoherence and dissipation for both fermions and cavity photons, and taking into account the varying coupling strength of different qubits to the cavity field and the spread of their transition frequencies. Compact analytic solutions for time-dependent quantum state amplitudes and observables are derived for a broad class of open quantum systems in Lindblad approximation with the use of the stochastic Schroedinger equation approach. We show that depending on the init…
Long-lived storage of arbitrary transverse multimodes is important for establishing a high-channel-capacity quantum network. Most of the pioneering works focused on atomic diffusion as the dominant impact on the retrieved pattern in an atom-based memory. In this work, we demonstrate that the unsynchronized Larmor precession of atoms in the inhomogeneous magnetic field dominates the distortion of the pattern stored in a cold-atom-based memory. We find that this distortion effect can be eliminated by applying a strong uniform polarization magnetic field. By preparing atoms in magnetically insens…
We study the ability to control d-dimensional quantum systems (qudits) encoded in the hyperfine spin of alkali-metal atoms through the application of radio- and microwave-frequency magnetic fields in the presence of inhomogeneities in amplitude and detuning. Such a capability is essential to the design of robust pulses that mitigate the effects of experimental uncertainty and also for application to tomographic addressing of particular members of an extended ensemble. We study the problem of preparing an arbitrary state in the Hilbert space from an initial fiducial state. We prove that inhomog…
We theoretically investigate the transport properties of a weak coherent input field scattered by an ensemble of $Λ$-type atoms coupled to a one-dimensional photonic crystal waveguide. In our model, the atoms are randomly located in the lattice along the crystal axis. We analyze the transmission spectrum mediated by the tunable long-range atomic interactions, and observe the highest-energy dip. The results show that the highest-energy dip location is associated with the number of the atoms, which provides an accurate measuring tool for the emitter-waveguide system. We also quantify the influen…
We propose a fast and non-destructive spectroscopic method for single molecular ions that implements quantum logic schemes between an atomic ion and the molecular ion of interest. Our proposal relies on a hybrid coherent manipulation of the two-ion system, using optical or magnetic forces depending on the types of molecular levels to be addressed (Zeeman, rotational, vibrational or electronic degrees of freedom). The method is especially suited for the non-destructive precision spectroscopy of single molecular ions, and sets a starting point for new hybrid quantum computation schemes that comb…
Compensation for parameter dispersion is a significant challenge for control of inhomogeneous quantum ensembles. In this paper, we present a systematic methodology of sampling-based learning control (SLC) for simultaneously steering the members of inhomogeneous quantum ensembles to the same desired state. The SLC method is employed for optimal control of the state-to-state transition probability for inhomogeneous quantum ensembles of spins as well as $Λ$ type atomic systems. The procedure involves the steps of (i) training and (ii) testing. In the training step, a generalized system is constru…
We propose a temporally multiplexed version of the Duan-Lukin-Cirac-Zoller (DLCZ) quantum repeater protocol using controlled inhomogeneous spin broadening in atomic gases. A first analysis suggests that the advantage of multiplexing is negated by noise due to spin wave excitations corresponding to unobserved directions of Stokes photon emission. However, this problem can be overcome with the help of a moderate-finesse cavity which is in resonance with Stokes photons, but invisible to the anti-Stokes photons. Our proposal promises greatly enhanced quantum repeater performance with atomic gases.
We experimentally demonstrate electromagnetically induced transparency and light storage with ultracold 87Rb atoms in a Mott insulating state in a three dimensional optical lattice. We have observed light storage times of about 240 ms, to our knowledge the longest ever achieved in ultracold atomic samples. Using the differential light shift caused by a spatially inhomogeneous far detuned light field we imprint a "phase gradient" across the atomic sample, resulting in controlled angular redirection of the retrieved light pulse.
The entanglement of multi-atom quantum states is considered. In order to cancel noise due to inhomogeneous light atom coupling, the concept of matched multi-atom observables is proposed. As a means to eliminate an important form of decoherence this idea should be of broad relevance for quantum information processing with atomic ensembles. The general approach is illustrated on the example of rotation angle measurement, and it is shown that the multi-atom states that were thought to be only weakly entangled can exhibit near-maximum entanglement.
The dynamics of a collection of resonant atoms embedded inside an inhomogeneous nondispersive and lossless dielectric is described with a dipole Hamiltonian that is based on a canonical quantization theory. The dielectric is described macroscopically by a position-dependent dielectric function and the atoms as microscopic harmonic oscillators. We identify and discuss the role of several types of Green tensors that describe the spatio-temporal propagation of field operators. After integrating out the atomic degrees of freedom, a multiple-scattering formalism emerges in which an exact Lippmann-S…
The ability to store multiple optical modes in a quantum memory allows for increased efficiency of quantum communication and computation. Here we compute the multimode capacity of a variety of quantum memory protocols based on light storage in ensembles of atoms. We find that adding a controlled inhomogeneous broadening improves this capacity significantly.
Implementation of the quantum interferometry concept to spin-1 atomic Bose-Einstein condensates is analyzed by employing a polar state evolved in time. In order to identify the best interferometric configurations, the quantum Fisher information is maximized. Three optimal configurations are identified, among which one was not reported in the literature yet, although it gives the highest value of the quantum Fisher information in experimentally achievable short time dynamics. Details of the most optimal configurations are investigated based on the error-propagation formula which includes the in…
We measure the sensitivity of a broadband atomic magnetometer using quantum non-demolition spin measurements. A cold, dipole-trapped sample of rubidium atoms provides a long-lived spin system in a non-magnetic environment, and is probed non-destructively by paramagnetic Faraday rotation. The calibration procedure employs a known reference state, the maximum-entropy or 'thermal' spin state and quantitative imaging-based atom counting to identify electronic, quantum, and technical noise in both the probe and spin system. The measurement achieves sensitivity 2.8 dB better than the projection nois…
We study the quantum dynamics of a single mode/particle interacting inhomogeneously with a large number of particles and introduce an effective approach to find the accessible Hilbert space where the dynamics takes place. Two relevant examples are given: the inhomogeneous Tavis-Cummings model (e.g., N atomic qubits coupled to a single cavity mode, or to a motional mode in trapped ions) and the inhomogeneous coupling of an electron spin to N nuclear spins in a quantum dot.
Laser spectroscopy of cold and trapped molecular ions is a powerful tool for fundamental physics, including the determination of fundamental constants, the laboratory test for their possible variation, and the search for a possible electric dipole moment of the electron. Optical clocks based on molecular ions sensitive to some of these effects are expected to achieve uncertainties approaching the $10^{-18}$ level. While the complexity of molecular structure facilitates these applications, the absence of cycling transitions poses a challenge for direct laser cooling, quantum state control, and …
The few-fermion atomic gas is an ideal setting to explore inhomogeneous superfluid pairing analogous to the Larkin-Ovchinnikov state. Two up and one down-spin atom is the minimal configuration that displays an inhomogeneous pairing density whereas imbalanced systems containing more fermions present a more complex pairing topology. With more than eight atoms trapped the system approaches the macroscopic superfluid limit. An oblate trap with a central barrier offers a direct experimental probe of pairing inhomogeneity.
Continuous change of the propagation direction of a classical control field in the process of its off-resonant Raman interaction with a weak signal field in a three-level atomic medium is suggested for quantum storage of a single-photon wave packet. It is shown that due to phase matching condition such an angular control allows one to reversibly map the single-photon wave packet to the Raman spatial coherence grating. Thus, quantum storage and retrieval can be realized without using inhomogeneous broadening of the atomic transitions or manipulating the amplitude of the control field. Under som…
