PHYSICAL REVIEW A

Proposed experiment to measure nonlinear optical susceptibilities in the saturated regime
Levine ZH
When an optical beam passes through a thin slice of a homogeneous material, the change of its phase and amplitude is characterized by the material's linear and nonlinear susceptibility, the latter also known as the hyperpolarizability. The standard method for measuring the nonlinear susceptibility is the scan. This widely used method is sometimes applied outside of its range of validity, leading to systematic errors. These errors are illustrated for a two-level system with parameters taken from atomic rubidium. The present paper proposes a method called the phase retrieval of modes to determine the nonlinear susceptibility without an assumption about its functional form, in contrast to both the -scan method and variants intended to apply in cases of saturation. In brief, a Gaussian beam passes through a thin sample and is detected on three planes in a focal scan. Phase retrieval methods are used to find coefficients of the modes which in turn determine the optical nonlinear susceptibility. Nearly exact recovery of the nonlinear susceptibility is shown numerically in the no-noise case. Additionally, two types of noise are considered: shot noise on the detector and intensity fluctuations of the input.
Emission Ghost Imaging: reconstruction with data augmentation
Coakley KJ, Chen-Mayer HH, Ravel B, Josell D, Klimov NN, Hussey DS and Robinson SM
Ghost Imaging enables 2D reconstruction of an object even though particles transmitted or emitted by the object of interest are detected with a single pixel detector without spatial resolution. This is possible because for the particular implementation of ghost imaging presented here, the incident beam is spatially modulated with a non-configurable attenuating mask whose orientation is varied (e.g. via transverse displacement or rotation) in the course of the ghost imaging experiment. Each orientation yields a distinct spatial pattern in the attenuated beam. In many cases, ghost imaging reconstructions can be dramatically improved by factoring the measurement matrix which consists of measured attenuated incident radiation for each of many orientations of the mask at each pixel to be reconstructed as the product of an orthonormal matrix and an upper triangular matrix provided that the number of orientations of the mask () is greater than or equal to the number of pixels () reconstructed. For the case, we present a data augmentation method that enables factorization of the measurement matrix. To suppress noise in the reconstruction, we determine the Moore-Penrose pseudoinverse of the measurement matrix with a truncated singular value decomposition approach. Since the resulting reconstruction is still noisy, we denoise it with the Adaptive Weights Smoothing method. In simulation experiments, our method outperforms a modification of an existing alternative orthogonalization method where rows of the measurement matrix are orthogonalized by the Gram-Schmidt method. We apply our ghost imaging methods to experimental X-ray fluorescence data acquired at Brookhaven National Laboratory.
Constraints on Gaussian Error Channels and Measurements for Quantum Communication
Kwiatkowski A, Shojaee E, Agrawal S, Kyle A, Rau CL, Glancy S and Knill E
Joint Gaussian measurements of two quantum systems are important for quantum communication between remote parties and are often used in continuous-variable teleportation or entanglement-swapping protocols. Many of the errors in real-world implementations can be modeled by independent Gaussian error channels acting prior to measurement. In this work we study independent single-mode Gaussian error channels on two modes A and B that take place prior to a joint Gaussian measurement. We determine the set of pairs of such channels that render all Gaussian measurements separable, and therefore unsuitable for entanglement swapping or teleportation of arbitrary input states. For example, if the error channels are loss with parameters followed by added noise with parameters then all Gaussian measurements are separable if and only if .
Measurement of electric-field noise from interchangeable samples with a trapped-ion sensor
McKay KS, Hite DA, Kent PD, Kotler S, Leibfried D, Slichter DH, Wilson AC and Pappas DP
We demonstrate the use of a single trapped ion as a sensor to probe electric-field noise from interchangeable test surfaces. As proof of principle, we measure the magnitude and distance dependence of electric-field noise from two ion-trap-like samples with patterned Au electrodes. This trapped-ion sensor could be combined with other surface characterization tools to help elucidate the mechanisms that give rise to electric-field noise from ion-trap surfaces. Such noise presents a significant hurdle for performing large-scale trapped-ion quantum computations.
Optimal measurement of field properties with quantum sensor networks
Qian T, Bringewatt J, Boettcher I, Bienias P and Gorshkov AV
We consider a quantum sensor network of qubit sensors coupled to a field ( ; ) analytically parameterized by the vector of parameters . The qubit sensors are fixed at positions , …, . While the functional form of ( ; ) is known, the parameters are not. We derive saturable bounds on the precision of measuring an arbitrary analytic function ( ) of these parameters and construct the optimal protocols that achieve these bounds. Our results are obtained from a combination of techniques from quantum information theory and duality theorems for linear programming. They can be applied to many problems, including optimal placement of quantum sensors, field interpolation, and the measurement of functionals of parametrized fields.
Improved coupled-mode theory for high-index-contrast photonic platforms
Li Q, Moille G, Taheri H, Adibi A and Srinivasan K
Coupled-mode theory (CMT) has been widely used in optics and photonics design. Despite its popularity, several different formulations of CMT exist in the literature, and their applicable range is not entirely clear, in particular when it comes to high-index-contrast photonics platforms. Here we propose an improved formulation of CMT and demonstrate its superior performance through numerical simulations that compare CMT-derived quantities with supermode calculations and full wave propagation simulations. In particular, application of the improved CMT to asymmetric waveguides reveals a necessary correction in the conventional phase matching condition for high-index-contrast systems, which could lead to more accurate photonic circuit designs involving asymmetric elements.
Phase-coherent sensing of the center-of-mass motion of trapped-ion crystals
Affolter M, Gilmore KA, Jordan JE and Bollinger JJ
Trapped ions are sensitive detectors of weak forces and electric fields that excite ion motion. Here measurements of the center-of-mass motion of a trapped-ion crystal that are phase coherent with an applied weak external force are reported. These experiments are conducted far from the trap motional frequency on a two-dimensional trapped-ion crystal of approximately 100 ions, and determine the fundamental measurement imprecision of our protocol free from noise associated with the center-of-mass mode. The driven sinusoidal displacement of the crystal is detected by coupling the ion crystal motion to the internal spin degree of freedom of the ions using an oscillating spin-dependent optical dipole force. The resulting induced spin precession is proportional to the displacement amplitude of the crystal, and is measured with near-projection-noise-limited resolution. A 49 pm displacement is detected with a signal-to-noise ratio of 1 in a single experimental determination, which is an order-of-magnitude improvement over prior phase-incoherent experiments. This displacement amplitude is 40 times smaller than the zero-point fluctuations. With our repetition rate, an displacement sensitivity is achieved, which implies and sensitivities to forces and electric fields, respectively. This displacement sensitivity, when applied on-resonance with the center-of-mass mode, indicates the possibility of weak force and electric field detection below 10 yNion and 1 nVm, respectively.
Broadening of the drumhead-mode spectrum due to in-plane thermal fluctuations of two-dimensional trapped ion crystals in a Penning trap
Shankar A, Tang C, Affolter M, Gilmore K, Dubin DHE, Parker S, Holland MJ and Bollinger JJ
Two-dimensional crystals of ions stored in Penning traps are a leading platform for quantum simulation and sensing experiments. For small amplitudes, the out-of-plane motion of such crystals can be described by a discrete set of normal modes called the drumhead modes, which can be used to implement a range of quantum information protocols. However, experimental observations of crystals with Doppler-cooled and even near-ground-state-cooled drumhead modes reveal an unresolved drumhead-mode spectrum. In this work, we establish in-plane thermal fluctuations in ion positions as a major contributor to the broadening of the drumhead-mode spectrum. In the process, we demonstrate how the confining magnetic field leads to unconventional in-plane normal modes, whose average potential and kinetic energies are not equal. This property, in turn, has implications for the sampling procedure required to choose the in-plane initial conditions for molecular-dynamics simulations. For current operating conditions of the NIST Penning trap, our study suggests that the two-dimensional crystals produced in this trap undergo in-plane potential-energy fluctuations of the order of 10mK. Our study therefore motivates the need for designing improved techniques to cool the in-plane degrees of freedom.
Nature of the nonequilibrium phase transition in the non-Markovian driven Dicke model
Lundgren R, Gorshkov AV and Maghrebi MF
The Dicke model famously exhibits a phase transition to a superradiant phase with a macroscopic population of photons and is realized in multiple settings in open quantum systems. In this paper, we study a variant of the Dicke model where the cavity mode is lossy due to the coupling to a Markovian environment while the atomic mode is coupled to a colored bath. We analytically investigate this model by inspecting its low-frequency behavior via the Schwinger-Keldysh field theory and carefully examine the nature of the corresponding superradiant phase transition. Integrating out the fast modes, we can identify a simple effective theory allowing us to derive analytical expressions for various critical exponents including the dynamical exponent. We find excellent agreement with previous numerical results when the non-Markovian bath is at zero temperature; however, contrary to these studies, our low-frequency approach reveals that the same exponents govern the critical behavior when the colored bath is at finite temperature unless the chemical potential is zero. Furthermore, we show that the superradiant phase transition is classical in nature, while it is genuinely nonequilibrium. We derive a fractional Langevin equation and conjecture the associated fractional Fokker-Planck equation that captures the system's long-time memory as well as its nonequilibrium behavior. Finally, we consider finite-size effects at the phase transition and identify the finite-size scaling exponents, unlocking a rich behavior in both statics and dynamics of the photonic and atomic observables.
Quantum simulation of hyperbolic space with circuit quantum electrodynamics: From graphs to geometry
Boettcher I, Bienias P, Belyansky R, Kollár AJ and Gorshkov AV
We show how quantum many-body systems on hyperbolic lattices with nearest-neighbor hopping and local interactions can be mapped onto quantum field theories in continuous negatively curved space. The underlying lattices have recently been realized experimentally with superconducting resonators and therefore allow for a table-top quantum simulation of quantum physics in curved background. Our mapping provides a computational tool to determine observables of the discrete system even for large lattices, where exact diagonalization fails. As an application and proof of principle we quantitatively reproduce the ground state energy, spectral gap, and correlation functions of the noninteracting lattice system by means of analytic formulas on the Poincaré disk, and show how conformal symmetry emerges for large lattices. This sets the stage for studying interactions and disorder on hyperbolic graphs in the future. Importantly, our analysis reveals that even relatively small discrete hyperbolic lattices emulate the continuous geometry of negatively curved space, and thus can be used to experimentally resolve fundamental open problems at the interface of interacting many-body systems, quantum field theory in curved space, and quantum gravity.
Enhanced transport of spin-orbit-coupled Bose gases in disordered potentials
Yue Y, de Melo CARS and Spielman IB
Anderson localization is a single-particle localization phenomena in disordered media that is accompanied by an absence of diffusion. Spin-orbit coupling (SOC) describes an interaction between a particle's spin and its momentum that directly affects its energy dispersion, for example, creating dispersion relations with gaps and multiple local minima. We show theoretically that combining one-dimensional spin-orbit coupling with a transverse Zeeman field suppresses the effects of disorder, thereby increasing the localization length and conductivity. This increase results from a suppression of backscattering between states in the gap of the SOC dispersion relation. Here, we focus specifically on the interplay of disorder from an optical speckle potential and SOC generated by two-photon Raman processes in quasi-one-dimensional Bose-Einstein condensates. We first describe backscattering by using a Fermi golden rule approach, and then numerically confirm this picture by solving the time-dependent one-dimensional Gross-Pitaevskii equation for a weakly interacting Bose-Einstein condensate with SOC and disorder. We find that on the tens of millisecond timescale of typical cold atom experiments moving in harmonic traps, initial states with momentum in the zero-momentum SOC gap evolve with negligible backscattering, while without SOC these same states rapidly localize.
Generating Greenberger-Horne-Zeilinger states with squeezing and postselection
Alexander B, Bollinger JJ and Uys H
Many quantum state preparation methods rely on a combination of dissipative quantum state initialization followed by unitary evolution to a desired target state. Here we demonstrate the usefulness of quantum measurement as an additional tool for quantum state preparation. Starting from a pure separable multipartite state, a control sequence, which includes rotation, spin squeezing via one-axis twisting, quantum measurement, and postselection, generates highly entangled multipartite states, which we refer to as (PS) states. Through an optimization method, we then identify parameters required to maximize the overlap fidelity of the PS states with the maximally entangled Greenberger-Horne-Zeilinger (GHZ) states. The method leads to an appreciable decrease in the state preparation time of GHZ states for successfully postselected outcomes when compared to preparation through unitary evolution with one-axis twisting only.
Competition between Factors Determining Bright versus Dark Atomic States within a Laser Mode
Hemingway B, Akin TG, Peil S and Porto JV
We observe bimodal fluorescence patterns from atoms in a fast atomic beam when the laser excitation occurs in the presence of a magnetic field and the atoms sample only a portion of the laser profile. The behavior is well explained by competition between the local intensity of the laser, which tends to generate a coherent-population-trapping (CPT) dark state in the = 1 to ' = 0 system, and the strength of an applied magnetic field that can frustrate the CPT process. This work is relevant for understanding and optimizing the detection process for clocks or other coherent systems utilizing these transitions and could be applicable to calibration of the laser-atom interaction, such as the strength of the magnetic field or laser intensity at a specific location.
Creating solitons with controllable and near-zero velocity in Bose-Einstein condensates
Fritsch AR, Lu M, Reid GH, Piñeiro AM and Spielman IB
Established techniques for deterministically creating dark solitons in repulsively interacting atomic Bose-Einstein condensates (BECs) can only access a narrow range of soliton velocities. Because velocity affects the stability of individual solitons and the properties of soliton-soliton interactions, this technical limitation has hindered experimental progress. Here we create dark solitons in highly anisotropic cigar-shaped BECs with arbitrary position and velocity by simultaneously engineering the amplitude and phase of the condensate wave function, improving upon previous techniques which explicitly manipulated only the condensate phase. The single dark soliton solution present in true one-dimensional (1D) systems corresponds to the kink soliton in anisotropic three-dimensional systems and is joined by a host of additional dark solitons, including vortex ring and solitonic vortex solutions. We readily create dark solitons with speeds from zero to half the sound speed. The observed soliton oscillation frequency suggests that we imprinted solitonic vortices, which for our cigar-shaped system are the only stable solitons expected for these velocities. Our numerical simulations of 1D BECs show this technique to be equally effective for creating kink solitons when they are stable. We demonstrate the utility of this technique by deterministically colliding dark solitons with domain walls in two-component spinor BECs.
Dielectronic resonances of and series in highly charged -shell tungsten ions
Dipti , Borovik A, Silwal R, Dreiling JM, Gall AC, Takacs E and Ralchenko Y
We present spectroscopic measurements and detailed theoretical analysis of inner-shell and dielectronic resonances in highly charged -shell ions of tungsten. The x-ray emission from through was recorded at the electron-beam ion trap (EBIT) facility at the National Institute of Standards and Technology with a high-purity Ge detector for electron-beam energies between 6.8 and 10.8 keV. The measured spectra clearly show the presence of strong resonance features as well as direct excitation spectral lines. The analysis of the recorded spectra with large-scale collisional-radiative modeling of the EBIT plasma allowed us to unambiguously identify numerous dielectronic resonances associated with excitations of the inner-shell , , and electrons.
Signaling and scrambling with strongly long-range interactions
Guo AY, Tran MC, Childs AM, Gorshkov AV and Gong ZX
Strongly long-range interacting quantum systems-those with interactions decaying as a power law 1/ in the distance on a -dimensional lattice for ⩽ -have received significant interest in recent years. They are present in leading experimental platforms for quantum computation and simulation, as well as in theoretical models of quantum-information scrambling and fast entanglement creation. Since no notion of locality is expected in such systems, a general understanding of their dynamics is lacking. In a step towards rectifying this problem, we prove two Lieb-Robinson-type bounds that constrain the time for signaling and scrambling in strongly long-range interacting systems, for which no tight bounds were previously known. Our first bound applies to systems mappable to free-particle Hamiltonians with long-range hopping, and is saturable for ⩽ /2. Our second bound pertains to generic long-range interacting spin Hamiltonians and gives a tight lower bound for the signaling time to extensive subsets of the system for all < . This many-site signaling time lower bounds the scrambling time in strongly long-range interacting systems.
Open System Tensor Networks and Kramers' Crossover for Quantum Transport
Wójtowicz G, Elenewski JE, Rams MM and Zwolak M
Tensor networks are a powerful tool for many-body ground states with limited entanglement. These methods can nonetheless fail for certain time-dependent processes-such as quantum transport or quenches-where entanglement growth is linear in time. Matrix-product-state decompositions of the resulting out-of-equilibrium states require a bond dimension that grows exponentially, imposing a hard limit on simulation timescales. However, in the case of transport, if the reservoir modes of a closed system are arranged according to their scattering structure, the entanglement growth can be made logarithmic. Here, we apply this ansatz to open systems via extended reservoirs that have explicit relaxation. This enables transport calculations that can access steady states, time dynamics and noise, and periodic driving (e.g., Floquet states). We demonstrate the approach by calculating the transport characteristics of an open, interacting system. These results open a path to scalable and numerically systematic many-body transport calculations with tensor networks.
Coherent optical nanotweezers for ultracold atoms
Bienias P, Subhankar S, Wang Y, Tsui TC, Jendrzejewski F, Tiecke T, Juzeliūnas G, Jiang L, Rolston SL, Porto JV and Gorshkov AV
There has been a recent surge of interest and progress in creating subwavelength free-space optical potentials for ultracold atoms. A key open question is whether geometric potentials, which are repulsive and ubiquitous in the creation of subwavelength free-space potentials, forbid the creation of narrow traps with long lifetimes. Here, we show that it is possible to create such traps. We propose two schemes for realizing subwavelength traps and demonstrate their superiority over existing proposals. We analyze the lifetime of atoms in such traps and show that long-lived bound states are possible. This work allows for subwavelength control and manipulation of ultracold matter, with applications in quantum chemistry and quantum simulation.
Doppler-Free Two-Photon Cavity Ring-Down Spectroscopy of a Nitrous Oxide (NO) Vibrational Overtone Transition
Zhao G, Bailey DM, Fleisher AJ, Hodges JT and Lehmann KK
We report Doppler-free two-photon absorption of NO at = 4.53 μm, measured by cavity ring-down spectroscopy. High power was achieved by optical self-locking of a quantum cascade laser to a linear resonator of finesse , and accurate laser detuning over a 400 MHz range was measured relative to an optical frequency comb. At a sample pressure of = 0.13 kPa, we report a large two-photon cross-section per molecule of cm s for the (18) rovibrational transition at a resonant frequency of = 66179400.8 MHz.
Certified Quantum Measurement of Majorana Fermions
Irfan AAM, Mayer K, Ortiz G and Knill E
We present a quantum self-testing protocol to certify measurements of fermion parity involving Majorana fermion modes. We show that observing a set of ideal measurement statistics implies anti-commutativity of the implemented Majorana fermion parity operators, a necessary prerequisite for Majorana detection. Our protocol is robust to experimental errors. We obtain lower bounds on the fidelities of the state and measurement operators that are linear in the errors. We propose to analyze experimental outcomes in terms of a contextuality witness , which satisfies 〈〉 ≤ 3 for any classical probabilistic model of the data. A violation of the inequality witnesses quantum contextuality, and the closeness to the maximum ideal value 〈〉 = 5 indicates the degree of confidence in the detection of Majorana fermions.
Collisions of room-temperature helium with ultracold lithium and the van der Waals bound state of HeLi
Makrides C, Barker DS, Fedchak JA, Scherschligt J, Eckel S and Tiesinga E
We have computed the thermally averaged total, elastic rate coefficient for the collision of a room-temperature helium atom with an ultracold lithium atom. This rate coefficient has been computed as part of the characterization of a cold-atom vacuum sensor based on laser-cooled Li or Li atoms that will operate in the ultrahigh-vacuum ( < 10 Pa) and extreme-high-vacuum ( < 10 Pa) regimes. The analysis involves computing the Σ HeLi Born-Oppenheimer potential followed by the numerical solution of the relevant radial Schrodinger equation. The potential is computed using a single-reference-coupled-cluster electronic-structure method with basis sets of different completeness in order to characterize our uncertainty budget. We predict that the rate coefficient for a 300 K helium gas and a 1 K Li gas is 1.467(13) × 10 cm/s for He + Li and 1.471(13) × 10 cm/s for He + Li, where the numbers in parentheses are the one-standard-deviation uncertainties in the last two significant digits. We quantify the temperature dependence as well. Finally, we evaluate the -wave scattering length and binding of the single van der Waals bound state of HeLi. We predict that this weakly bound level has a binding energy of -0.0064(43) × cm and -0.0122(67) × cm for HeLi and HeLi, respectively. The calculated binding energy of HeLi is consistent with the sole experimental determination.