We propose a scheme for trapped atom interferometry using an interacting Bose-Einstein condensate. The condensate is controlled and spatially split in two confined external momentum modes through a series Bragg pulses. The proposed scheme (i) allows the generation of large entanglement in a trapped-interferometer configuration via one-axis twisting dynamic induced by interatomic interaction, and (ii) avoids the suppression of interactions during the interferometer sequence by a careful manipulation of the state before and after phase encoding. The interferometer can be used for the measurement of gravity with a sensitivity beyond the standard quantum limit.
We present a detailed study of the effects of imperfect atom-optical manipulation in Bragg-based light-pulse atom interferometers. Off-resonant higher-order diffraction leads to population loss, spurious interferometer paths, and diffraction phases. In a path-dependent formalism, we study numerically various effects and analyze the interference signal caused by an external phase or gravity. We compare first-order single and double Bragg diffraction in retroreflective setups. In double Bragg diffraction, phase imperfections lead to a beating due to three-path interference. Some effects of diffr…
We have constructed an atom interferometer of the Mach-Zehnder type, operating with a supersonic beam of lithium. Atom diffraction uses Bragg diffraction on laser standing waves. With first order diffraction, our apparatus has given a large signal and a very good fringe contrast (74%), which we believe to be the highest ever observed with atom interferometers. This apparatus will be applied to high sensitivity measurements
We provide a comprehensive study of ultra-cold atom diffraction by an optical lattice. We focus on an intermediate regime between the Raman-Nath and the Bragg regimes, the so-called quasi-Bragg regime. The experimental results are in a good agreement with a full numerical integration of the Schrödinger equation. We investigate the long pulse regime limited by a strong velocity selection and the short pulse regime limited by non-adiabatic losses. For each of these regimes, we estimate the multi-port features of the Bragg interferometers. Finally, we discuss the best compromise between these two…
We present the experimental implementation of double Bragg diffraction of Bose-Einstein condensates (BECs) as proposed in [E. Giese, A. Roura, G. Tackmann, E. M. Rasel, and W. P. Schleich, Phys. Rev. A \textbf{88}, 053608 (2013)]. We excite Rabi oscillations between the three coupled momentum states $\left| 0 \hbar k \right\rangle$ and $\left| \pm 2 \hbar k \right\rangle$. By selecting appropriate interaction times we generate highly efficient beamsplitters and mirrors for Bose-Einstein condensates. In addition, we demonstrate higher-order double Bragg diffraction and display beamsplitters wit…
We theoretically analyze the Bragg spectroscopic interferometer of two spatially separated atomic Bose-Einstein condensates that was experimentally realized by Saba et al. [Science 2005 v307 p1945] by continuously monitoring the relative phase evolution. Even though the atoms in the light-stimulated Bragg scattering interact with intense coherent laser beams, we show that the phase is created by quantum measurement-induced back-action on the homodyne photo-current of the lasers, opening possibilities for quantum-enhanced interferometric schemes. We identify two regimes of phase evolution: a ru…
A magnetic field gradient applied to an atom interferometer induces a $M$-dependent phase shift which results in a series of decays and revivals of the fringe visibility. Using our lithium atom interferometer based on Bragg laser diffraction, we have measured the fringe visibility as a function of the applied gradient. We have thus tested the isotopic selectivity of the interferometer, the velocity selective character of Bragg diffraction for different diffraction orders as well as the effect of optical pumping of the incoming atoms. All these observations are qualitatively understood but a qu…
Bragg interferometers, operating using pseudospin-1/2 systems composed of two momentum states, have become a mature technology for precision measurements. State-of-the-art Bragg interferometers are rapidly surpassing technical limitations and are soon expected to operate near the projection noise limit set by uncorrelated atoms. Despite the use of large numbers of atoms, their operation is governed by single-atom physics. Motivated by recent proposals and demonstrations of Raman gravimeters in cavities, we propose a scheme to squeeze directly on momentum states for surpassing the projection no…
A method for mitigating the readout delay characteristic of Bragg-based atom interferometry is presented, utilizing an asymmetric Mach-Zehnder interferometer sequence to generate spatial fringes that are read out while still overlapped. The time of flight after the final beamsplitter is engineered to facilitate constructive overlap of the fringes on the output states. A noise analysis performed using a precision atom interferometer is presented, comparing the traditional separated symmetric scheme with that of the separated and overlapped asymmetric scheme showing no significant increase in sh…
We theoretically consider the effect of the atomic source's momentum width on the efficiency of Bragg mirrors and beamsplitters and, more generally, on the phase sensitivity of Bragg pulse atom interferometers. By numerical optimization, we show that an atomic cloud's momentum width places a fundamental upper bound on the maximum transfer efficiency of a Bragg mirror pulse, and furthermore limits the phase sensitivity of a Bragg pulse atom interferometer. We quantify these momentum width effects, and precisely compute how mirror efficiencies and interferometer phase sensitivities vary as funct…
We present a precision gravimeter based on coherent Bragg diffraction of freely falling cold atoms. Traditionally, atomic gravimeters have used stimulated Raman transitions to separate clouds in momentum space by driving transitions between two internal atomic states. Bragg interferometers utilize only a single internal state, and can therefore be less susceptible to environmental perturbations. Here we show that atoms extracted from a magneto-optical trap using an accelerating optical lattice are a suitable source for a Bragg atom interferometer, allowing efficient beamsplitting and subsequen…
We present a method for rapid prototyping of new Bragg ultra-cold atom interferometer (AI) designs useful for assessing the performance of such interferometers. The method simulates the overall effect on the condensate wave function in a given AI design using two separate elements. These are (1) modeling the effect of a Bragg pulse on the wave function and (2) approximating the evolution of the wave function during the intervals between the pulses. The actual sequence of these pulses and intervals is then followed to determine the approximate final wave function from which the interference pat…
We propose a configuration of a magnetic microtrap which can be used as an interferometer for three-dimensionally trapped atoms. The interferometer is realized via a dynamic splitting potential that transforms from a single well into two separate wells and back. The ports of the interferometer are neighboring vibrational states in the single well potential. We present a one-dimensional model of this interferometer and compute the probability of unwanted vibrational excitations for a realistic magnetic potential. We optimize the speed of the splitting process in order suppress these excitations…
We show how an experimentally realized set of operations on a single trapped ion is sufficient to simulate a wide class of Hamiltonians of a spin-1/2 particle in an external potential. This system is also able to simulate other physical dynamics. As a demonstration, we simulate the action of an $n$-th order nonlinear optical beamsplitter. Two of these beamsplitters can be used to construct an interferometer sensitive to phase shifts in one of the interferometer beam paths. The sensitivity in determining these phase shifts increases linearly with $n$, and the simulation demonstrates that the us…
Bragg diffraction is comparable to a hard-wall reflection if the Bragg condition is exactly fulfilled. However, in a neutron interferometer in the gravitational field (COW experiment) this is not the case and the momentum transfers should not be described by hard wall reflection, as it has been done in the commented article. Instead, and quite similar to the atom case, each mirror or beam splitter creates a constant momentum transfer given by the reciprocal lattice vector of the Bragg crystal. To lowest order there are no differences between the atom and the neutron case.
We have built and operated an atom interferometer of the Mach-Zehnder type. The atomic wave is a supersonic beam of lithium seeded in argon and the mirrors and beam-splitters for the atomic wave are based on elastic Bragg diffraction on laser standing waves at 671 nm. We give here a detailed description of our experimental setup and of the procedures used to align its components. We then present experimental signals, exhibiting atomic interference effects with a very high visibility, up to 84.5 %. We describe a series of experiments testing the sensitivity of the fringe visibility to the main …
We propose an interferometric measurement of weak forces using a single ion subjected to designed time-dependent spin-dependent forces. Explicit expressions of the relation between the unknown force and the final populations are found considering different scenarios, such as the weak force acting on two branches, on one branch, or having errors in the driving force. The flexibility to design the trap trajectories is used to minimize errors due to anharmonicities in the trap. The advantages of the approach are the use of geometrical phases, which provides stability, the possibility to design fa…
We report experimental observations of large Bragg reflection from arrays of cold atoms trapped near a one-dimensional nanoscale waveguide. By using an optical lattice in the evanescent field surrounding a nanofiber with a period nearly commensurate with the resonant wavelength, we observe a reflectance of up to 75% for the guided mode. Each atom behaves as a partially-reflecting mirror and an ordered chain of about 2000 atoms is sufficient to realize an efficient Bragg mirror. Measurements of the reflection spectra as a function of the lattice period and the probe polarization are reported. T…
A Sagnac atom interferometer can be constructed using a Bose-Einstein condensate trapped in a cylindrically symmetric harmonic potential. Using the Bragg interaction with a set of laser beams, the atoms can be launched into circular orbits, with two counterpropagating interferometers allowing many sources of common-mode noise to be excluded. In a perfectly symmetric and harmonic potential, the interferometer output would depend only on the rotation rate of the apparatus. However, deviations from the ideal case can lead to spurious phase shifts. These phase shifts have been theoretically analyz…
In this work we propose a novel single-atom interferometer based on a fully two-dimensional spatial adiabatic passage process using a system of three identical harmonic traps in a triangular geometry. While the transfer of a single atom from the ground state of one trap to the ground state of the most distant one can successfully be achieved in a robust way for a broad range of parameter values, we point out the existence of a specific geometrical configuration of the traps for which a crossing of two energy eigenvalues occurs and the transfer of the atom fails. Instead the wavefunction is rob…
We propose a compact atom interferometer to measure homogeneous constant forces guiding the arms via shortcuts to adiabatic paths. For a given sensitivity, which only depends on the space-time area of the guiding paths, the cycle time can be made fast without loosing visibility. The atom is driven by spin-dependent trapping potentials moving in opposite directions, complemented by linear and time-dependent potentials that compensate the trap acceleration. Thus the arm states are adiabatic in the moving frames, and non-adiabatic in the laboratory frame. The trapping potentials may be anharmonic…
The beam splitter and phase shifter, which are the key elements in the experiments of light interference, are realized in the motion of trapped ions. Some applications, such as the creation of quantum motional states and the realization of Mach-Zehnder interferometer, are illustrated. Several detection methods of motional states used in the interferometer are also discussed.
We study the best attainable measurement precision when a double-well trap with bosons inside acts as an interferometer to measure the energy difference of the atoms on the two sides of the trap. We introduce time independent perturbation theory as the main tool in both analytical arguments and numerical computations. Nonlinearity from atom-atom interactions will not indirectly allow the interferometer to beat the Heisenberg limit, but in many regimes of the operation the Heisenberg limit scaling of measurement precision is preserved in spite of added tunneling of the atoms and atom-atom inter…
We present a free-space interferometer to observe two-particle interference of a pair of atoms with entangled momenta. The source of atom pairs is a Bose--Einstein condensate subject to a dynamical instability, and the interferometer is realized using Bragg diffraction on optical lattices, in the spirit of our recent Hong--Ou--Mandel experiment. We report an observation consistent with an entangled state at the input of the interferometer. We explain how our current setup can be extended to enable a test of a Bell inequality on momentum observables.
Rotation of atoms in a lattice is studied using a Hubbard model. It is found that the atoms are still contained in the trap even when the rotation frequency is larger than the trapping frequency. This is very different from the behavior in continuum. Bragg scattering and coupling between angular and radial motion are believed to make this stability possible. In this regime, density depletion at the center of the trap can be developed for spin polarized fermions.
Sagnac interferometers with massive particles promise unique advantages in achieving high precision measurements of rotation rates over their optical counterparts. Recent proposals and experiments are exploring non-ballistic Sagnac interferometers where trapped atoms are transported along a closed path. This is achieved by using superpositions of internal quantum states and their control with state-dependent potentials. We address emergent questions regarding the dynamical behavior of Bose-Einstein condensates in such an interferometer and its impact on rotation sensitivity. We investigate com…
Quantum information processing with geometric features of quantum states may provide promising noise-resilient schemes for quantum metrology. In this work, we theoretically explore phase-space geometric Sagnac interferometers with trapped atomic clocks for rotation sensing, which could be intrinsically robust to certain decoherence noises and reach high precision. With the wave guide provided by sweeping ring-traps, we give criteria under which the well-known Sagnac phase is a pure or unconventional geometric phase with respect to the phase space. Furthermore, corresponding schemes for geometr…
We have performed a precision atomic interferometry experiment on testing the universality of free fall (UFF) considering atoms' spin degree of freedom. Our experiment employs the Bragg atom interferometer with $^{87}$Rb atoms either in hyperfine state $\left| {F = 1,{m_F} = 0} \right\rangle $ or $\left| {F = 2,{m_F} = 0} \right\rangle $, and the wave packets in these two states are diffracted in one pair of Bragg beams alternatively, which can help suppress the common-mode systematic errors. We have obtained an E$\rm{\ddot{o}}$tv$\rm{\ddot{o}}$s ratio $η= \left( { 0.9 \pm 2.7} \right) \times …
We report a theoretical study of a double-well Ramsey interferometer using internal state labelling. We consider the use of a thermal ensemble of cold atoms rather than a Bose-Einstein condensate to minimize the effects of atomic interactions. To maintain a satisfactory level of coherence in this case, a high degree of symmetry is required between the two arms of the interferometer. Assuming that the splitting and recombination processes are adiabatic, we theoretically derive the phase-shift and the contrast of such an interferometer in the presence of gravity or an acceleration field. We also…
We explore the possibility of implementing a Heisenberg-limited Mach-Zehnder interferometry via an array of trapped ions, which obey a quantum Ising model within a transverse field. Based upon adiabatic processes of increasing the Ising interaction and then decreasing the transverse field, we demonstrate a perfect transition from paramagnetism to ferromagnetic states, which can be used as the beam splitter for the multi-ion Mach-Zehnder interferometry. The achieved NOON state of the ions enables the Heisenberg-limited interferometry. Using currently available techniques for ultracold ions, we …
High-fidelity Bragg pulses are an indispensable tool for state-of-the-art atom interferometry experiments. In this paper, we introduce an analytic theory for such pulses. Our theory is based on the pivotal insight that the physics of Bragg pulses can be accurately described by the adiabatic theorem. We show that efficient Bragg diffraction is possible with any smooth and adiabatic pulse shape and that high-fidelity Gaussian pulses are exclusively adiabatic. Our results give strong evidence that adiabaticity according to the adiabatic theorem is a necessary requirement for high-performance Brag…
The use of retro-reflection in light-pulse atom interferometry under microgravity conditions naturally leads to a double-diffraction scheme. The two pairs of counterpropagating beams induce simultaneously transitions with opposite momentum transfer that, when acting on atoms initially at rest, give rise to symmetric interferometer configurations where the total momentum transfer is automatically doubled and where a number of noise sources and systematic effects cancel out. Here we extend earlier implementations for Raman transitions to the case of Bragg diffraction. In contrast with the single…
We demonstrate bi-chromatic adiabatic magnetic shell traps as a novel tool for matterwave interferometry. Using two strong RF fields, we dress the $|1,-1\rangle $ and $ |2,1\rangle$ states of Rubidium Bose-Einstein Condensates thus creating two independently controllable shell traps. This allows us to match the two traps and, using microwave pulses, create a state-dependent clock-type interferometer. Given the low horizontal confinement of the interferometer, the atoms can be made to spread out thus yielding a 2D sheet, which could be used in a direct imaging interferometer. This interferomete…
We study an ultra-cold gas of $N$ bosons trapped in a one dimensional $M$-site optical lattice perturbed by a spatially dependent potential $g\cdot x^j$, where the unknown coupling strength $g$ is to be estimated. We find that the measurement uncertainty is bounded by $Δg\propto\frac1{N (M^j-1)}$. For a typical case of a linear potential, the sensitivity improves as $M^{-1}$, which is a result of multiple interferences between the sites -- an advantage of multi-path interferometers over the two-mode setups. Next, we calculate the estimation sensitivity for a specific measurement where, after t…
We demonstrate an all-fiber cavity QED system with a trapped single atom in the strong coupling regime. We use a nanofiber Fabry-Perot cavity, that is, an optical nanofiber sandwiched by two fiber-Bragg-grating mirrors. Measurements of the cavity transmission spectrum with a single atom in a state-insensitive nanofiber trap clearly reveal the vacuum Rabi splitting.
We study the dynamics of Bose-Einstein condensates in time-dependent microtraps for the purpose of understanding the influence of the mean field interaction on the performance of interferometers. We identify conditions where the non-linearity due to atom interactions increases the sensitivity of interferometers to a phase shift. This feature is connected with the adiabatic generation of a dark soliton. We analyze the robustness of this phenomenon with respect to thermal fluctuations, due to excited near fields in an electromagnetic surface trap.
Collective spins of large atomic samples trapped inside optical resonators can carry quantum information that can be processed in a way similar to quantum computation with continuous variables. It is shown here that by combining the resonators in multi-path interferometers one can realize coupling between different samples, and that polynomial Hamiltonians can be constructed by repeated spin rotations and twisting induced by dispersive interaction of the atoms with light. Application can be expected in efficient simulation of quantum systems.
The extreme miniaturization of a cold-atom interferometer accelerometer requires the development of novel technologies and architectures for the interferometer subsystems. Here we describe several component technologies and a laser system architecture to enable a path to such miniaturization. We developed a custom, compact titanium vacuum package containing a microfabricated grating chip for a tetrahedral grating magneto-optical trap (GMOT) using a single cooling beam. In addition, we designed a multi-channel photonic-integrated-circuit-compatible laser system implemented with a single seed la…
This paper presents the first realisation of a simultaneous $^{87}$Rb -$^{85}$Rb Mach-Zehnder atom interferometer with Bose-condensed atoms. A number of ambitious proposals for precise terrestrial and space based tests of the Weak Equivalence Principle rely on such a system. This implementation utilises hybrid magnetic-optical trapping to produce spatially overlapped condensates with a duty cycle of 20s. A horizontal optical waveguide with co-linear Bragg beamsplitters and mirrors is used to simultaneously address both isotopes in the interferometer. We observe a non-linear phase shift on a no…
We show how to implement a Mach-Zehnder interferometry based upon a string of trapped ions with artificial nonlinear interactions. By adiabatically sweeping down/up the coupling strength between two involved internal states of the ions, we could achieve the beam splitting/recombination. Based on current techniques for manipulating trapped ions, we discuss the experimental feasibility of our scheme and analyze some undesired uncertainty under realistic experimental environment.
We demonstrate a dual-axis accelerometer and gyroscope atom interferometer, which forms the building blocks of a six-axis inertial measurement unit. By recapturing the atoms after the interferometer sequence, we maintain a large atom number at high data-rates of 50 to 100 measurements per second. Two cold ensembles are formed in trap zones located a few centimeters apart, and are launched toward one-another. During their ballistic trajectory, they are interrogated with a stimulated Raman sequence, detected, and recaptured in the opposing trap zone. We achieve sensitivities at $\mathrm{μ\mathit…
We present a protocol for using trapped ions to measure rotations via matter-wave Sagnac interferometry. The trap allows the interferometer to enclose a large area in a compact apparatus through repeated round-trips in a Sagnac geometry. We show how a uniform magnetic field can be used to close the interferometer over a large dynamic range in rotation speed and measurement bandwidth without losing contrast. Since this technique does not require the ions to be confined in the Lamb-Dicke regime, thermal states with many phonons should be sufficient for operation.
