Precision metrology and quantum measurement often demand matter be prepared in well defined quantum states for both internal and external degrees of freedom. Laser-cooled neutral atoms localized in a deeply confining optical potential satisfy this requirement. With an appropriate choice of wavelength and polarization for the optical trap, two electronic states of an atom can experience the same trapping potential, permitting coherent control of electronic transitions independent of the atomic center-of-mass motion. We review a number of recent experiments that use this approach to investigate precision quantum metrology for optical atomic clocks and coherent control of optical interactions of single atoms and photons within the context of cavity quantum electrodynamics. We also provide a brief survey of promising prospects for future work.
We present the characterization of a prototype surface-electrode (SE) trap as a first step towards the realization of a compact, single-ion optical clock based on Yb$^+$. The use of a SE trap will be a key factor to benefit from clean-room fabrication techniques and technological advances made in the field of quantum information processing. We succesfully demonstrated trapping at a 500 $μ$m electrodes distance and characterized our trap in terms of lifetime and heating rate. This is to our knowledge the highest distance achieved for heating rates measurements in SE traps. This simple 5-wire de…
We propose a scheme for state-insensitive trapping of neutral atoms by using light with two independent wavelengths. In particular, we describe the use of trapping and control lasers to minimize the variance of the potential experienced by a trapped Rb atom in ground and excited states. We present calculated values of wavelength pairs for which the 5s and 5p_{3/2} levels have the same ac Stark shifts in the presence of two laser fields.
We demonstrate near-complete cancellation of the differential light shift of a two-photon magnetic-field-insensitive microwave hyperfine (clock) transition in $^{87}$Rb atoms trapped in an optical lattice. Up to $95(2)%$ of the differential light shift is canceled while maintaining magnetic-field insensitivity. This technique should have applications in quantum information and frequency metrology.
Sub-Planck phase-space structures in the Wigner function of the motional degree of freedom of a trapped ion can be used to perform weak force measurements with Heisenberg-limited sensitivity. We propose methods to engineer the Hamiltonian of the trapped ion to generate states with such small scale structures, and we show how to use them in quantum metrology applications.
Advanced techniques for manipulation of internal states, standard in atomic physics, are demonstrated for a charged molecular species for the first time. We address individual hyperfine states of ro-vibrational levels of a diatomic ion by optical excitation of individual hyperfine transitions, and achieve controlled transfer of population into a selected hyperfine state. We use molecular hydrogen ions (HD^{+}) as a model system and employ a novel frequency-comb-based, continuous-wave 5 \mum laser spectrometer. The achieved spectral resolution is the highest obtained so far in the optical domai…
We have experimentally demonstrated that magnetic-field-insensitive coherent-population-trapping (CPT) resonances are generated between the ground hyperfine levels on the $D_1$ line of $^{133}$Cs using a two-photon $Λ$ scheme excited by lin || lin polarizations. The frequency shift of the CPT resonance is 0.04 Hz for the deviation of 1 $μ$T at a "magic" magnetic field of 139 $μ$T and is 50 times smaller than that of the conventional clock transition at a typical bias magnetic field for the clock operation. The amplitude of the CPT spectrum excited by lin || lin polarizations is enhanced as the…
We present an all optical technique to prepare a sample of $^{39}$K in a magnetically-insensitive state with 95\% purity while maintaining a temperature of 6 $μ$K. This versatile preparation scheme is particularly well suited to performing matter-wave interferometry with species exhibiting closely-separated hyperfine levels, such as the isotopes of lithium and potassium, and opens new possibilities for metrology with these atoms. We demonstrate the feasibility of such measurements by realizing an atomic gravimeter and a Ramsey-type spectrometer, both of which exhibit a state-of-the-art sensiti…
We report the experimental realization of an optical trap that localizes single Cs atoms ~215 nm from surface of a dielectric nanofiber. By operating at magic wavelengths for pairs of counter-propagating red- and blue-detuned trapping beams, differential scalar light shifts are eliminated, and vector shifts are suppressed by ~250. We thereby measure an absorption linewidth Γ/2π= 5.7 \pm 0.1 MHz for the Cs 6S1/2,F=4 - 6P3/2,F'=5 transition, where Γ/2π= 5.2 MHz in free space. Optical depth d~66 is observed, corresponding to an optical depth per atom d_1~0.08. These advances provide an important …
A ring crystal of ions trapped in a linear multipole trap is studied as a basis for an optical frequency standard. The equilibrium conditions and cooling possibilities are discussed through an analytical model and molecular dynamics simulations. A configuration which reduces the frequency sensitivity to the fluctuations of the number of trapped ions is proposed. The systematic shifts for the electric quadrupole transition of calcium ions are evaluated for this ring configuration. This study shows that a ring of 10 or 20 ions allows to reach a short term stability better than for a single ion w…
We briefly discuss recent experiments on quantum information processing using trapped ions at NIST. A central theme of this work has been to increase our capabilities in terms of quantum computing protocols, but we have also applied the same concepts to improved metrology, particularly in the area of frequency standards and atomic clocks. Such work may eventually shed light on more fundamental issues, such as the quantum measurement problem.
Laser trapping and interfacing of laser-cooled atoms in an optical fiber network is an important capability for quantum information science. Following the pioneering work of Balykin et al. and Vetsch et al., we propose a robust method of trapping single Cesium atoms with a two-color state-insensitive evanescent wave around a dielectric nanofiber. Specifically, we show that vector light shifts (i.e., effective inhomogeneous Zeeman broadening of the ground states) induced by the inherent ellipticity of the forward-propagating evanescent wave can be effectively canceled by a backward-propagating …
We show how to create quantum gates of arbitrary speed between trapped ions, using a laser walking wave, with complete insensitivity to drift of the optical phase, and requiring cooling only to the Lamb-Dicke regime. We present pulse sequences that satisfy the requirements and are easy to produce in the laboratory.
We examine a range of effects arising from ac magnetic fields in high precision metrology. These results are directly relevant to high precision measurements, and accuracy assessments for state-of-the-art optical clocks. Strategies to characterize these effects are discussed and a simple technique to accurately determine trap-induced ac magnetic fields in a linear Paul trap is demonstrated using $^{171}\mathrm{Yb}^+$
We calculate the optical potentials, i.e. the light shifts, of the ground and excited states of atomic cesium in a two-color evanescent field around a subwavelength-diameter fiber. We show that the light shifts of the $6S_{1/2}\leftrightarrow 6P_{3/2}$ transitions can be minimized by tuning one trapping light to around 934.5 nm in wavelength (central red-detuned magic wavelength) and the other light to around 685.5 nm in wavelength (central blue-detuned magic wavelength). The simultaneous use of the red- and blue-detuned magic wavelengths allows state-insensitive two-color trapping and guiding…
Single Cesium atoms are cooled and trapped inside a small optical cavity by way of a novel far-off-resonance dipole-force trap (FORT), with observed lifetimes of 2 to 3 seconds. Trapped atoms are observed continuously via transmission of a strongly coupled probe beam, with individual events lasting ~ 1 s. The loss of successive atoms from the trap N = 3 -> 2 -> 1 -> 0 is thereby monitored in real time. Trapping, cooling, and interactions with strong coupling are enabled by the FORT potential, for which the center-of-mass motion is only weakly dependent on the atom's internal state.
Entanglement is recognized as a key resource for quantum computation and quantum cryptography. For quantum metrology, the use of entangled states has been discussed and demonstrated as a means of improving the signal-to-noise ratio. In addition, entangled states have been used in experiments for efficient quantum state detection and for the measurement of scattering lengths. In quantum information processing, manipulation of individual quantum bits allows for the tailored design of specific states that are insensitive to the detrimental influences of an environment. Such 'decoherence-free subs…
A promising practical application of entanglement is metrology, where quantum states can be used to make measurements beyond the shot noise limit. Here we consider how metrology schemes could be realised using atomic Bose-Einstein condensates (BECs) trapped in different potentials. In particular, we show that if a trapped BEC is rotated at just the right frequency, it can undergo a quantum phase transition characterised by large-scale entanglement spreading across the system. This simple process of stirring can generate interesting quantum states such as macroscopic superpositions of all the a…
We analyze the properties of a pulsed Coherent Population Trapping protocol that uses a controlled decay from the excited state in a $Λ$-level scheme. We study this problem analytically and numerically and find regimes where narrow transmission, absorption, or fluorescence spectral lines occur. We then look for optimal frequency measurements using these spectral features by computing the Allan deviation in the presence of ground state decoherence and show that the protocol is on a par with Ramsey-CPT. We discuss possible implementations with ensembles of alkali atoms and single ions and demons…
Crosstalk Insensitive Trapped-Ion Entanglement through Coupling Matrix Engineering
Joint Center for Quantum Information and Computer Science, University of Maryland（马里兰大学量子信息与计算联合中心）；Department of Physics, University of Maryland（马里兰大学物理系）；Department of Electrical and Computer Engineering, University of Washington（华盛顿大学电气与计算机工程系）
We discuss theoretically the ground state of a Bose-Einstein condensate with attractive atom-atom interactions in a double-well trap as a starting point of Heisenberg-limited atom interferometry. The dimensionless parameter governing the quality of the ground state for this purpose is identified. The near-degeneracy between the ground state and the first excited state severely curtails the prospects of the thermally prepared ground state in quantum metrology.
We show that far field diffraction image of spontaneously scattered Stokes photons can be used for detection of spin entanglement and for metrology of fields gradients in cold atomic ensembles. For many-body states with small or maximum uncertainty in spin-excitation number, entanglement is simply witnessed by the presence of a sharp diffraction peak or dip. Gradient vector of external fields is measured by the displacement of a diffraction peak due to inhomogeneous spin precessions, which suggests a new possibility for precision measurement beyond the standard quantum limit without entangleme…
We achieve fast, nondestructive quantum-state readout via fluorescence detection of a single $^{87}$Rb atom in the 5$S_{1/2}$ ($F=2$) ground state held in an optical dipole trap. The atom is driven by linearly-polarized readout laser beams, making the scheme insensitive to the distribution of atomic population in the magnetic sub-levels. We demonstrate a readout fidelity of $97.6\pm0.2\%$ in a readout time of $160\pm20$ $μ$s with the atom retained in $>97\%$ of the trials, representing an advancement over other magnetic-state-insensitive techniques. We demonstrate that the $F=2$ state is parti…
Entangled states of rotating, trapped ultracold bosons form a very promising scenario for quantum metrology. In order to employ such states for metrology, it is vital to understand their detailed form and the enhanced accuracy with which they could measure phase, in this case generated through rotation. In this work we study the rotation of ultracold bosons in an asymmetric trapping potential beyond the lowest Landau level (LLL) approximation. We demonstrate that whilst the LLL can identify reasonably the critical frequency for a quantum phase transition and entangled state generation, it is v…
National Institute of Standards and Technology（美国国家标准与技术研究院）；British Columbia Institute of Technology（不列颠哥伦比亚理工学院）；University of Bremen（不来梅大学）；Physikalisch-Technische Bundesanstalt（德国联邦物理技术研究院）；University of Maryland（马里兰大学）；University of British Columbia（不列颠哥伦比亚大学）
Several errors in Refs. [1, 2] are corrected related to the optical trapping potentials for a state-insensitive, compensated nanofiber trap for the D2 transition of atomic Cesium. Section I corrects our basic formalism in Ref. [1] for calculating dipole-force potentials. Section II corrects erroneous values for a partial lifetime and a transition wavelength in Ref. [1]. Sections III and IV present corrected figures for various trapping configurations considered in Refs. [1] and [2], respectively.
We experimentally demonstrate an atom number detector capable of simultaneous detection of two mesoscopic ensembles with single-atom resolution. Such a sensitivity is a prerequisite for quantum metrology at a precision approaching the Heisenberg limit. Our system is based on fluorescence detection of atoms in a novel hybrid trap in which a dipole barrier divides a magneto-optical trap into two separated wells. We introduce a noise model describing the various sources contributing to the measurement error and report a limit of up to 500 atoms for single-atom resolution in the atom number differ…
We propose an optical scheme for generating entanglement between co-trapped identical or dissimilar alkaline earth atomic ions ($^{40}\text{Ca}^+$, $^{88}\text{Sr}^+$, $^{138}\text{Ba}^+$, $^{226}\text{Ra}^+$) which exhibits fundamental error rates below $10^{-4}$ and can be implemented with a broad range of laser wavelengths spanning from ultraviolet to infrared. We also discuss straightforward extensions of this technique to include the two lightest Group-2 ions ($\text{Be}^+$, $\text{Mg}^+$) for multispecies entanglement. The key elements of this wavelength-insensitive geometric phase gate …
Quantum technologies exploit entanglement to revolutionize computing, measurements, and communications. This has stimulated the research in different areas of physics to engineer and manipulate fragile many-particle entangled states. Progress has been particularly rapid for atoms. Thanks to the large and tunable nonlinearities and the well developed techniques for trapping, controlling and counting, many groundbreaking experiments have demonstrated the generation of entangled states of trapped ions, cold and ultracold gases of neutral atoms. Moreover, atoms can couple strongly to external forc…
Rydberg atoms are remarkable tools for quantum simulation and computation. They are the focus of an intense experimental activity mainly based on low-angular-momentum Rydberg states. Unfortunately, atomic motion and levels lifetime limit the experimental time-scale to about 100$μ$s. Here, we demonstrate laser trapping of long-lived circular Rydberg states for up to 10ms. Our method is very general and opens many opportunities for quantum simulation. The 10ms trapping time corresponds to thousands of interaction cycles in a circular-state-based quantum simulator. It is also promising for quantu…
We analyze doubly magic trapping of Cs hyperfine transitions including previously neglected contributions from the ground state hyperpolarizability and the interaction of the laser light and a static magnetic field. Extensive numerical searches do not reveal any doubly magic trapping conditions for any pair of hyperfine states. However, including the hyperpolarizability reveals light intensity insensitive traps for a wide range of wavelengths at specific intensities. We then investigate the possibility of using bichromatic trapping light fields. Deploying a bichromatic scheme, we demonstrate d…
We propose a versatile Loschmidt echo protocol to detect and quantify multiparticle entanglement. It allows us to extract the quantum Fisher information for arbitrary pure states, and finds direct application in quantum metrology. In particular, the protocol applies to states that are generally difficult to characterize, as non-Gaussian states, and states that are not symmetric under particle exchange. We focus on atomic systems, including trapped ions, polar molecules, and Rydberg atoms, where entanglement is generated dynamically via long-range interaction, and show that the protocol is stab…
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…
Microfabricated ion traps are a major advancement towards scalable quantum computing with trapped ions. The development of more versatile ion-trap designs, in which tailored arrays of ions are positioned in two dimensions above a microfabricated surface, would lead to applications in fields as varied as quantum simulation, metrology and atom-ion interactions. Current surface ion traps often have low trap depths and high heating rates, due to the size of the voltages that can be applied to them, limiting the fidelity of quantum gates. Here we report on a fabrication process that allows for the …
By utilizing Bose-Einstein condensate solitons, optically manipulated and trapped in a double-well potential, coupled through nonlinear Josephson effect, we propose novel quantum metrology applications with two soliton qubit states. In addition to steady-state solutions in different scenarios, phase space analysis, in terms of population imbalance - phase difference variables, is also performed to demonstrate macroscopic quantum self-trapping regimes. Schrödinger-cat states, maximally path-entangled ($N00N$) states, and macroscopic soliton qubits are predicted and exploited for the distinguish…
We develop a general theory to estimate magnetic field gradients in quantum metrology. We consider a system of $N$ particles distributed on a line whose internal degrees of freedom interact with a magnetic field. Usually gradient estimation is based on precise measurements of the magnetic field at two different locations, performed with two independent groups of particles. This approach, however, is sensitive to fluctuations of the off-set field determining the level-splitting of the particles and results in collective dephasing. In this work we use the framework of quantum metrology to assess…
We summarise important recent advances in quantum metrology, in connection to experiments in cold gases, trapped cold atoms and photons. First we review simple metrological setups, such as quantum metrology with spin squeezed states, with Greenberger-Horne-Zeilinger states, Dicke states and singlet states. We calculate the highest precision achievable in these schemes. Then, we present the fundamental notions of quantum metrology, such as shot-noise scaling, Heisenberg scaling, the quantum Fisher information and the Cramer-Rao bound. Using these, we demonstrate that entanglement is needed to s…
We describe a new type of blue detuned optical lattice for atom trapping which is intrinsically two dimensional, while providing three-dimensional atom localization. The lattice is insensitive to optical phase fluctuations since it does not depend on field interference between distinct optical beams. The array is created using a novel arrangement of weakly overlapping Gaussian beams that creates a two-dimensional array of dark traps which are suitable for magic trapping of ground and Rydberg states. We analyze the spatial localization that can be achieved and demonstrate trapping and detection…
Noise-Symmetry Optimization of Quantum Error-Corrected Metrology
School of Physics, Sun Yat-sen University（中山大学物理学院）；State Key Laboratory for Mesoscopic Physics, Department of Physics, Peking University（北京大学物理学院介观物理国家重点实验室）；Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）
By considering matter wave bright solitons from weakly coupled Bose-Einstein condensates trapped in a double-well potential, we study the formation of macroscopic non-classical states, including Schrödinger-cat superposition states and maximally path entangled $N00N$-states. With these macroscopic states, we examine Mach-Zehnder interferometer in the context of parity measurements, in order to obtain Heisenberg limit accuracy for linear phase shift measurement. We reveal that the ratio between two-body scattering length and intra-well hopping parameter can be measured with the scaling beyond t…
We discuss a quantum-metrology protocol designed to estimate a physical parameter in a Bose-Einstein condensate of N atoms, and we show that the measurement uncertainty can decrease faster than 1/N. The 1/N scaling is usually thought to be the best possible in any measurement scheme. From the perspective of quantum information theory, we outline the main idea that leads to a measurement uncertainty that scales better than 1/N. We examine in detail some potential problems and challenges that arise in implementing such a measurement protocol using a Bose-Einstein condensate. We discuss how some …
We examine the precision limits of Hong-Ou-Mandel (HOM) timing measurements, as well as precision limits applying to generalized two-photon measurements. As a special case, we consider the use of two-photon measurements using photons with variable bandwidths and frequency correlations. When the photon bandwidths are not equal, maximizing the measurement precision involves a trade-off between high interference visibility and strong frequency anticorrelations, with the optimal precision occuring when the photons share non-maximal frequency anticorrelations. We show that a generalized measurement…
Magnetic trapping is a cornerstone for modern ultracold physics and its applications (e.g., quantum information processing, quantum metrology, quantum optics, or high-resolution spectroscopies). Here a comprehensive analysis and discussion of the basic physics behind the most commonly used magnetic traps in Bose-Einstein condensation is presented. This analysis includes the quadrupole trap, the time-averaged orbiting potential trap, and the Ioffe-Pritchard trap. It is shown how the trapping conditions and efficiency of these devices can be determined from simple derivations based on classical …
Physikalisch-Technische Bundesanstalt（德国联邦物理技术研究院）；Deutsches Zentrum für Luft- und Raumfahrt (DLR) Institut für Satellitengeodäsie und Inertialsensorik（德国航空航天中心卫星测地与惯性传感器研究所）；Naturwissenschaftlich-Technische Fakultät, Universität Siegen（锡根大学理学院）；eleQtron GmbH（eleQtron有限公司）；Institut für Quantenoptik, Leibniz Universität Hannover（汉诺威莱布尼茨大学量子光学研究所）
We propose a new concept for a two-qubit gate operating on a pair of trapped ions based on laser coherent control techniques. The gate is insensitive to the temperature of the ions, works also outside the Lamb-Dicke regime, requires no individual addressing by lasers, and can be orders of magnitude faster than the trap period.
Quantum sensors are an established technology that has created new opportunities for precision sensing across the breadth of science. Using entanglement for quantum-enhancement will allow us to construct the next generation of sensors that can approach the fundamental limits of precision allowed by quantum physics. However, determining how state-of-the-art sensing platforms may be used to converge to these ultimate limits is an outstanding challenge. In this work we merge concepts from the field of quantum information processing with metrology, and successfully implement experimentally a *prog…
We propose a method to achieve scalable quantum computation based on fast quantum gates on an array of trapped ions, without the requirement of ion shuttling. Conditional quantum gates are obtained for any neighboring ions through spin-dependent acceleration of the ions from periodic photon kicks. The gates are shown to be robust to influence of all the other ions in the array and insensitive to the ions' temperature.
We show that the quasi-adiabatic evolution of a system governed by the Dicke Hamiltonian can be described in terms of a self-induced quantum many-body metrological protocol. This effect relies on the sensitivity of the ground state to a small symmetry-breaking perturbation at the quantum phase transition, that leads to the collapse of the wavefunciton into one of two possible ground states. The scaling of the final state properties with the number of atoms and with the intensity of the symmetry breaking field, can be interpreted in terms of the precession time of an effective quantum metrologi…
