We investigate a small vortex-lattice system of four corotating vortices in an atomic Bose-Einstein condensate and find that the vortex dynamics display chaotic behavior after a system quench introduced by reversing the direction of circulation of a single vortex through a phase-imprinting process. By tracking the vortex trajectories and Lyapunov exponent, we show the onset of chaotic dynamics is not immediate, but occurs at later times and is accelerated by the close approach and separation of all vortices in a scattering event. The techniques we develop could potentially be applied to create locally induced chaotic dynamics in larger lattice systems as a stepping stone to study the role of chaotic events in turbulent vortex dynamics.
The complex collisional properties of atoms fundamentally limit investigations into a range of processes in many-atom ensembles. In contrast, the bottom-up assembly of few- and many-body systems from individual atoms offers a controlled approach to isolating and studying such collisional processes. Here, we use optical tweezers to individually assemble pairs of trapped 85Rb atoms, and study the spin dynamics of the two-body system in a thermal state. The spin-2 atoms show strong pair correlation between magnetic sublevels on timescales exceeding one second, with measured relative number fluctuations 11.9 ± 0.3 dB below quantum shot noise, limited only by detection efficiency. Spin populations display relaxation dynamics consistent with simulations and theoretical predictions for 85Rb spin interactions, and contrary to the coherent spin waves witnessed in finite-temperature many-body experiments and zero-temperature two-body experiments. Our experimental approach offers a versatile platform for studying two-body quantum dynamics and may provide a route to thermally robust entanglement generation.
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 short-term phase noise.
The continuous monitoring of a quantum system strongly influences the emergence of chaotic dynamics near the transition from the quantum regime to the classical regime. Here we present a feedback control scheme that uses adaptive measurement techniques to control the degree of chaos in the driven-damped quantum Duffing oscillator. This control relies purely on the measurement backaction on the system, making it a uniquely quantum control, and is only possible due to the sensitivity of chaos to measurement. We quantify the effectiveness of our control by numerically computing the quantum Lyapunov exponent over a wide range of parameters. We demonstrate that adaptive measurement techniques can control the onset of chaos in the system, pushing the quantum-classical boundary further into the quantum regime.
We theoretically investigate the effect of multimode dynamics on the creation of macroscopic superposition states (spin-cat states) in Bose-Einstein condensates via one-axis twisting. A two-component Bose-Einstein condensate naturally realizes an effective one-axis twisting interaction, under which an initially separable state will evolve toward a spin-cat state. However, the large evolution times necessary to realize these states is beyond the scope of current experiments. This evolution time is proportional to the degree of asymmetry in the relative scattering lengths of the system, which results in the following trade-off: faster evolution times are associated with an increase in multimode dynamics, and we find that generally multimode dynamics reduce the degree of entanglement present in the final state. However, we find that highly entangled catlike states are still possible in the presence of significant multimode dynamics and that these dynamics impose a speed limit on the evolution of such states.
The transmission of an interacting Bose-Einstein condensate incident on a repulsive Gaussian barrier is investigated through numerical simulation. The dynamics associated with interatomic interactions are studied across a broad parameter range not previously explored. Effective one-dimensional Gross-Pitaevskii equation (GPE) simulations are compared to classical Boltzmann-Vlasov equation (BVE) simulations in order to isolate purely coherent matter-wave effects. Quantum tunneling is then defined as the portion of the GPE transmission not described by the classical BVE. An exponential dependence of transmission on barrier height is observed in the classical simulation, suggesting that observing such an exponential dependence is not a sufficient condition for quantum tunneling. Furthermore, the transmission is found to be predominately described by classical effects, although interatomic interactions are shown to modify the magnitude of the quantum tunneling. Interactions are also seen to affect the amount of classical transmission, producing transmission in regions where the noninteracting equivalent has none. This theoretical investigation clarifies the contribution quantum tunneling makes to overall transmission in many-particle interacting systems, potentially informing future tunneling experiments with ultracold atoms.
We calculate quantum and classical Fisher information for gravity sensors based on matter-wave interference, and find that current Mach-Zehnder interferometry is not optimally extracting the full metrological potential of these sensors. We show that by making measurements that resolve either the momentum or the position we can considerably improve the sensitivity. We also provide a simple modification that is capable of more than doubling the sensitivity.
This paper presents 1.6 MHz scan rate, non-intrusive, time-resolved temperature measurements of a normal shock reflection from a plane end wall within a shock tube. A vertical-cavity surface-emitting laser (VCSEL) was used to conduct tunable diode laser absorption spectroscopy with water vapor as the probe species. The results are compared with analytical predictions. Temperatures measured with this technique agree within a single-scan standard deviation of ±33 K with calculated temperatures at a VCSEL modulation frequency of 800 kHz, which is sufficiently rapid enough to be used to investigate highly transient shock wave interaction processes.
We observe the breakup dynamics of an elongated cloud of condensed 85Rb atoms placed in an optical waveguide. The number of localized spatial components observed in the breakup is compared with the number of solitons predicted by a plane-wave stability analysis of the nonpolynomial nonlinear Schrödinger equation, an effective one-dimensional approximation of the Gross-Pitaevskii equation for cigar-shaped condensates. It is shown that the numbers predicted from the fastest growing sidebands are consistent with the experimental data, suggesting that modulational instability is the key underlying physical mechanism driving the breakup.
Stationary and slow light effects are of great interest for quantum information applications. Using laser-cooled Rb87 atoms, we performed side imaging of our atomic ensemble under slow and stationary light conditions, which allows direct comparison with numerical models. The polaritons were generated using electromagnetically induced transparency (EIT), with stationary light generated using counter-propagating control fields. By controlling the power ratio of the two control fields, we show fine control of the group velocity of the stationary light. We also compare the dynamics of stationary light using monochromatic and bichromatic control fields. Our results show negligible difference between the two situations, in contrast to previous work in EIT-based systems.
The precise control of atom–light interactions is vital to many quantum technologies. For instance, atomic systems can be used to slow and store light, acting as a quantum memory. Optical storage can be achieved via stopped light, where no optical energy continues to exist in the atomic system, or as stationary light, where some optical energy remains present during storage. Here, we demonstrate a form of self-stabilizing stationary light. From any initial state, our atom–light system evolves to a stable configuration that may contain bright optical excitations trapped within the atomic ensemble. This phenomenon is verified experimentally in a cloud of cold Rb87 atoms. The spinwave in our atomic cloud is imaged from the side, allowing direct comparison with theoretical predictions.
Resonant frequency modulation imaging is used to detect free falling ultra-cold atoms. A theoretical comparison of fluorescence imaging (FI) and frequency modulation imaging (FMI) is made, indicating that for low optical depth clouds, FMI accomplished a higher signal-to-noise ratio under conditions necessary for a 200 μm spatially resolved atom interferometer. A 750 ms time-of-flight measurement reveals near atom shot-noise limited number measurements of 2×106 Bose-condensed 87Rb atoms. The detection system is applied to high precision spinor BEC based atom interferometer.
We apply an online optimization process based on machine learning to the production of Bose-Einstein condensates (BEC). BEC is typically created with an exponential evaporation ramp that is optimal for ergodic dynamics with two-body s-wave interactions and no other loss rates, but likely sub-optimal for real experiments. Through repeated machine-controlled scientific experimentation and observations our ‘learner’ discovers an optimal evaporation ramp for BEC production. In contrast to previous work, our learner uses a Gaussian process to develop a statistical model of the relationship between the parameters it controls and the quality of the BEC produced. We demonstrate that the Gaussian process machine learner is able to discover a ramp that produces high quality BECs in 10 times fewer iterations than a previously used online optimization technique. Furthermore, we show the internal model developed can be used to determine which parameters are essential in BEC creation and which are unimportant, providing insight into the optimization process of the system.
A Bose-Einstein condensate is used as an atomic source for a high precision sensor. A 5×106 atom F=1 spinor condensate of 87Rb is released into free fall for up to 750 ms and probed with a T=130 ms Mach-Zehnder atom interferometer based on Bragg transitions. The Bragg interferometer simultaneously addresses the three magnetic states |mf=1,0,−1⟩, facilitating a simultaneous measurement of the acceleration due to gravity with a 1000 run precision of Δg/g=1.45×10−9 and the magnetic field gradient to a precision of 120 pT/m.
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 Rb85, the technique generalizes to other atomic species and is shown to be capable of a signal-to-noise of ~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 with a fast optical phase locked loop, the system is capable of dynamically switching to resonant absorption imaging during the experiment.
Optical quantum memory is an essential element for long-distance quantum communication and photonic quantum computation protocols. The practical implementation of such protocols requires an efficient quantum memory with a long coherence time. Beating the no-cloning limit, for example, requires efficiencies above 50%. An ideal optical fiber loop has a loss of 50% in 100 μs, and until now no universal quantum memory has beaten this time efficiency limit. Here, we report results of a gradient echo memory experiment in a cold atomic ensemble with a 1∕e coherence time up to 1 ms and maximum efficiency up to 87% +/- 2% for short storage times. Our experimental data demonstrate greater than 50% efficiency for storage times up to 0.6 ms. Quantum storage ability is verified beyond the ideal fiber limit using heterodyne tomography of small coherent states.
This roadmap bundles fast developing topics in experimental optical quantum sciences, addressing current challenges as well as potential advances in future research. We have focused on three main areas: quantum assisted high precision measurements, quantum information/simulation, and quantum gases. Quantum assisted high precision measurements are discussed in the first three sections, which review optical clocks, atom interferometry, and optical magnetometry. These fields are already successfully utilized in various applied areas. We will discuss approaches to extend this impact even further. In the quantum information/simulation section, we start with the traditionally successful employed systems based on neutral atoms and ions. In addition the marvelous demonstrations of systems suitable for quantum information is not progressing, unsolved challenges remain and will be discussed. We will also review, as an alternative approach, the utilization of hybrid quantum systems based on superconducting quantum devices and ultracold atoms. Novel developments in atomtronics promise unique access in exploring solid-state systems with ultracold gases and are investigated in depth. The sections discussing the continuously fast-developing quantum gases include a review on dipolar heteronuclear diatomic gases, Rydberg gases, and ultracold plasma. Overall, we have accomplished a roadmap of selected areas undergoing rapid progress in quantum optics, highlighting current advances and future challenges. These exciting developments and vast advances will shape the field of quantum optics in the future.
We introduce a scheme for the parallel storage of frequency separated signals in an optical memory and demonstrate that this dual-rail storage is a suitable memory for high fidelity frequency qubits. The two signals are stored simultaneously in the Zeeman-split Raman absorption lines of a cold atom ensemble using gradient echo memory techniques. Analysis of the split-Zeeman storage shows that the memory can be configured to preserve the relative amplitude and phase of the frequency separated signals. In an experimental demonstration dual-frequency pulses are recalled with 35% efficiency, 82% interference fringe visibility, and 6° phase stability. The fidelity of the frequency-qubit memory is limited by frequency-dependent polarisation rotation and ambient magnetic field fluctuations, our analysis describes how these can be addressed in an alternative configuration.
We present the first realization of a solitonic atom interferometer. A Bose-Einstein condensate of 1 × 104 atoms of rubidium-85 is loaded into a horizontal optical waveguide. Through the use of a Feshbach resonance, the s-wave scattering length of the 85Rb atoms is tuned to a small negative value. This attractive atomic interaction then balances the inherent matter-wave dispersion, creating a bright solitonic matter wave. A Mach-Zehnder interferometer is constructed by driving Bragg transitions with the use of an optical lattice colinear with the waveguide. Matter-wave propagation and interferometric fringe visibility are compared across a range of s-wave scattering values including repulsive, attractive and noninteracting values. The solitonic matter wave is found to significantly increase fringe visibility even compared with a noninteracting cloud.
This paper presents the first realization of a simultaneous 87Rb–85Rb 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 utilizes hybrid magnetic-optical trapping to produce spatially overlapped condensates with a repetition rate of 20 s. 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 non-interacting 85Rb interferometer as a function of interferometer time, T, which we show arises from inter-isotope scattering with the co-incident 85Rb interferometer. A discussion of implications for future experiments is given.
Atom interferometers have been used to measure acceleration with at best a T2 scaling in sensitivity as the interferometer time T is increased. This limits the sensitivity to acceleration which is theoretically achievable by these configurations for a given frequency of acceleration. We predict and experimentally measure the acceleration-sensitive phase shift of a large-momentum-transfer atom interferometer based upon Bloch oscillations. Using this novel interferometric scheme we demonstrate an improved scaling of sensitivity which will scale as T3. This enhanced scaling will allow an increase in achievable sensitivity for any given frequency of an oscillatory acceleration signal, which will be of particular use for inertial and navigational sensors, and proposed gravitational wave detectors. A straightforward extension should allow a T4 scaling in acceleration sensitivity.
The role of source cloud spatial coherence in a Mach-Zehnder-type atom interferometer is experimentally investigated. The visibility and contrast of a Bose-Einstein condensate (BEC) and three thermal sources with varying spatial coherence are compared as a function of interferometer time. At short times, the fringe visibility of a BEC source approaches 100% nearly independent of π pulse efficiency, while thermal sources have fringe visibilities limited to the π pulse efficiency. More importantly for precision measurement systems, the BEC source maintains interference at interferometer times significantly beyond the thermal source.
Since their development in the late 1980s, cheap, reliable external cavity diode lasers (ECDLs) have replaced complex and expensive traditional dye and Titanium Sapphire lasers as the workhorse laser of atomic physics labs1,2. Their versatility and prolific use throughout atomic physics in applications such as absorption spectroscopy and laser cooling1,2 makes it imperative for incoming students to gain a firm practical understanding of these lasers. This publication builds upon the seminal work by Wieman3, updating components, and providing a video tutorial. The setup, frequency locking and performance characterization of an ECDL will be described. Discussion of component selection and proper mounting of both diodes and gratings, the factors affecting mode selection within the cavity, proper alignment for optimal external feedback, optics setup for coarse and fine frequency sensitive measurements, a brief overview of laser locking techniques, and laser linewidth measurements are included.
Two simple external cavity diode laser designs using fibre pigtailed gain chips are tested and their properties compared with a high end DBR fibre laser. These ECDLs demonstrate a FWHM linewidth as low as 5.2kHz with a fitted Lorentzian FWHM linewidth as low as 1.6kHz. Tuning ranges of 200nm covering 1420nm to 1620nm were demonstrated. To the best of our knowledge these are the narrowest linewidth and most broadly tunable external cavity diode lasers reported to date. The improvement in linewidth is attributed to greatly enhanced acoustic isolation allowed by using fiber coupled gain chips and by replacing kinematic mounts with a pair of rotatable wedges for cavity alignment which eliminates acoustic resonances. A detailed description and discussion of techniques used to characterize the frequency noise and linewidths of these lasers is provided.
We report on the delay of optical pulses using electromagnetically induced transparency (EIT) in an ensemble of cold atoms with an optical depth exceeding 500. To identify the regimes in which four-wave mixing (4WM) impacts on EIT behaviour, we conduct the experiment in both 85Rb and 87Rb. Comparison with theory shows excellent agreement in both isotopes. In 87Rb negligible 4WM was observed and we obtained one pulse-width of delay with 50% efficiency. In 85Rb 4WM contributes to the output. In this regime we achieve a delay-bandwidth product of 3.7 at 50% efficiency, allowing temporally multimode delay, which we demonstrate by compressing two pulses into the memory medium.
Quantum memories for light lie at the heart of long-distance provably-secure communication. Demand for a functioning quantum memory, with high efficiency and coherence times approaching a millisecond, is therefore at a premium. Here we report on work towards this goal, with the development of a 87Rb magneto-optical trap with a peak optical depth of 1000 for the D2 F = 2 → F' = 3 transition using spatial and temporal dark spots. With this purpose-built cold atomic ensemble we implemented the gradient echo memory (GEM) scheme on the D1 line. Our data shows a memory efficiency of 80 ± 2% and coherence times up to 195 μs.
We demonstrate phase sensitivity in a horizontally guided, acceleration-sensitive atom interferometer with a momentum separation of 80ℏk between its arms. A fringe visibility of 7% is observed. Our coherent pulse sequence accelerates the cold cloud in an optical waveguide, an inherently scalable route to large momentum separation and high sensitivity. We maintain coherence at high momentum separation due to both the transverse confinement provided by the guide and our use of optical δ-kick cooling on our cold-atom cloud. We also construct a horizontal interferometric gradiometer to measure the longitudinal curvature of our optical waveguide.
Quantum memories are an integral component of quantum repeaters—devices that will allow the extension of quantum key distribution to communication ranges beyond that permissible by passive transmission. A quantum memory for this application needs to be highly efficient and have coherence times approaching a millisecond. Here we report on work towards this goal, with the development of a 87Rb magneto-optical trap with a peak optical depth of 1000 for the D2 F = 2 → F' = 3 transition using spatial and temporal dark spots. With this purpose-built cold atomic ensemble we implemented the gradient echo memory (GEM) scheme on the D1 line. Our data shows a memory efficiency of 80 ± 2% and coherence times up to 195 μs, which is a factor of four greater than previous GEM experiments implemented in warm vapour cells.
We review experimental progress on atom lasers out-coupled from Bose–Einstein condensates, and consider the properties of such beams in the context of precision inertial sensing. The atom laser is the matter-wave analogue of the optical laser. Both devices rely on Bose-enhanced scattering to produce a macroscopically populated trapped mode that is output-coupled to produce an intense beam. In both cases, the beams often display highly desirable properties such as low divergence, high spectral flux and a simple spatial mode that make them useful in practical applications, as well as the potential to perform measurements at or below the quantum projection noise limit. Both devices display similar second-order correlations that differ from thermal sources. Because of these properties, atom lasers are a promising source for application to precision inertial measurements.
For centuries, humans have measured time by counting oscillations of highly regular periodic motion—the Sun, a pendulum, or a quartz crystal, for example. During the past 50 years, we have chosen to use the electromagnetic oscillations, which drive absorption in an atom—a highly stable and universal frequency reference. Such atomic clocks define the SI second via an atomic resonance in cesium (1). The second is the most precisely defined physical unit. Although it may seem obvious now, making the leap from performing precise spectroscopy on the atomic structure of cesium to using its atomic structure as a precise reference to stabilize other oscillators was profound. On page 554 of this issue, Lan et al. (2) make an analogous distinction between performing momentum-spectroscopy on a recoiling atom, and using that spectroscopy to stabilize an oscillator, effectively locking a clock to the mass of a particle. This result has important implications for fundamental physics and precision measurement, and could play a role in a new definition of the kilogram.
We demonstrate a horizontal, linearly guided Mach-Zehnder atom interferometer in an optical waveguide. Intended as a proof-of-principle experiment, the interferometer utilizes a Bose-Einstein condensate in the magnetically insensitive |F = 1, mF = 0 ⟩ state of 87Rb as an acceleration-sensitive test mass. We achieve a modest sensitivity to acceleration of Δa = 7 × 10−4 m/s2. Our fringe visibility is as high as 38 % in this optically guided atom interferometer. We observe a time of flight in the waveguide of over 0.5 s, demonstrating the utility of our optical guide for future sensors.
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 subsequent separation of momentum states for detection. Despite the inherently multi-state nature of atom diffraction, we are able to build a Mach–Zehnder interferometer using Bragg scattering which achieves a sensitivity to the gravitational acceleration of Δg/g = 2.7 × 10−9 with an integration time of 1000 s. The device can also be converted to a gravity gradiometer by a simple modification of the light pulse sequence.
Over 250 years ago Sir Isaac Newton, inspired by an apple falling from a tree in his orchard (Stuckeley 1752), made the mental leap to conjecture that the same force that caused this apple to fall also held the Moon to the Earth. This stimulated him to develop his Law of Gravitation, and led to the principle that all objects fall with the same acceleration irrespective of their mass, as observed by Galileo Galilei. Over 250 years ago, these scientists understood gravity as well as many people do today. In reality, we still measure gravity by dropping a proverbial apple – a falling test mass whose trajectory we measure through space–time. However, developments over the past two centuries have led to a vast improvement in our measurement precision. With the advent of the optical laser and atom interferometers over the past 50 years, we have far superior rulers, and far superior clocks with which to make such a measurement.
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 functions of Bragg order and source type. Our results and methodology allow for an efficient optimization of Bragg pulses and the comparison of different atomic sources, and will help in the design of large momentum transfer Bragg mirrors and beamsplitters for use in atom-based inertial sensors.
We present a narrow linewidth continuous laser source with over 11 W output power at 780 nm, based on single-pass frequency doubling of an amplified 1560 nm fibre laser with 36% efficiency. This source offers a combination of high power, simplicity, mode quality and stability. Without any active stabilization, the linewidth is measured to be below 10 kHz. The fibre seed is tunable over 60 GHz, which allows access to the D2 transitions in 87Rb and 85Rb, providing a viable high-power source for laser cooling as well as for large-momentum-transfer beamsplitters in atom interferometry. Sources of this type will pave the way for a new generation of high flux, high duty-cycle degenerate quantum gas experiments.
We numerically analyze the quantum efficiency and dark noise of a cavity-based single-atom detector, with particular emphasis on the ability to measure number squeezing in an atom-laser beam. We consider the influence of the electric-dipole force on an atom in a red-detuned detection beam and discuss the much improved detection efficiency for detuned probe beams, with respect to resonant probes, resulting from this influence. Cavities allow real-time monitoring of atomic flux, with single-atom resolution, but they are much slower than their analog in photonics (the avalanche photodiode), so flux limits must be imposed. The proposed detector operates at a maximum flux of 5000 atoms/second, but with a shot-noise clearance of up to 23 dB, allowing the full advantage afforded by number squeezing to be observed.
In a light-pulse atom interferometer, we use a tip-tilt mirror to remove the inﬂuence of the Coriolis force from Earth’s rotation and to characterize conﬁguration space wave packets. For interferometers with a large momentum transfer and large pulse separation time, we improve the contrast by up to 350% and suppress systematic effects. We also reach what is to our knowledge the largest space-time area enclosed in any atom interferometer to date. We discuss implications for future high-performance instruments.
We present a cold-atom gravimeter operating with a sample of Bose-condensed 87Rb atoms. Using a Mach-Zehnder configuration with the two arms separated by a two-photon Bragg transition, we observe interference fringes with a visibility of (83 ± 6)% at T = 3 ms. We exploit large momentum transfer (LMT) beam splitting to increase the enclosed space-time area of the interferometer using higher-order Bragg transitions and Bloch oscillations. We also compare fringes from condensed and thermal sources and observe a reduced visibility of (58 ± 4)% for the thermal source. We suspect the loss in visibility is caused partly by wave-front aberrations, to which the thermal source is more susceptible due to its larger transverse momentum spread. Finally, we discuss briefly the potential advantages of using a coherent atomic source for LMT, and we present a simple mean-field model to demonstrate that with currently available experimental parameters, interaction-induced dephasing will not limit the sensitivity of inertial measurements using freely falling, coherent atomic sources.
We present a Ramsey-type atom interferometer operating with an optically trapped sample of 106 Bose-condensed 87Rb atoms. We investigate this interferometer experimentally and theoretically with an eye to the construction of future high precision atomic sensors. Our results indicate that, with further experimental refinements, it will be possible to produce and measure the output of a sub-shot-noise-limited, large atom number BEC-based interferometer. The optical trap allows us to couple the |F=1, mF=0⟩→|F=2, mF=0⟩ clock states using a single photon 6.8 GHz microwave transition, while state selective readout is achieved with absorption imaging. We analyse the process of absorption imaging and show that it is possible to observe atom number variance directly, with a signal-to-noise ratio ten times better than the atomic projection noise limit on 106 condensate atoms. We discuss the technical and fundamental noise sources that limit our current system, and present theoretical and experimental results on interferometer contrast, de-phasing and miscibility.
Collapsing Bose-Einstein condensates are rich and complex quantum systems for which quantitative explanation by simple models has proved elusive. We present experimental data on the collapse of high-density 85Rb condensates with attractive interactions and find quantitative agreement with the predictions of the Gross-Pitaevskii equation. The collapse data and measurements of the decay of atoms from our condensates allow us to put new limits on the value of the 85Rb three-body loss coefficient K3 at small positive and negative scattering lengths.
In our original paper (Altin et al 2011 New J. Phys. 13 065020), we presented the results from a Ramsey atom interferometer operating with an optically trapped sample of up to 106 Bose-condensed 87Rb atoms in the mF = 0 clock states. We were unable to observe projection noise fluctuations on the interferometer output, which we attribute to the stability of our microwave oscillator and background magnetic field. Numerical simulations of the Gross–Pitaevskii equations for our system show that dephasing due to spatial dynamics driven by interparticle interactions accounts for much of the observed decay in fringe visibility at long interrogation times. The simulations show good agreement with the experimental data when additional technical decoherence is accounted for, and suggest that the clock states are indeed immiscible. With smaller samples of 5 × 104 atoms, we observe a coherence time of τ = 1.0+0.5−0.3 s.
Every measurement of the population in an uncorrelated ensemble of two-level systems is limited by what is known as the quantum projection noise limit. Here, we present quantum-projection-noise-limited performance of a Ramsey-type interferometer using freely propagating coherent atoms. The experimental setup is based on an electro-optic modulator in an inherently stable Sagnac interferometer, optically coupling the two interfering atomic states via a two-photon Raman transition. Going beyond the quantum projection noise limit requires the use of reduced quantum uncertainty (squeezed) states. The experiment described demonstrates atom interferometry at the fundamental noise level and allows the observation of possible squeezing effects in an atom laser, potentially leading to improved sensitivity in atom interferometers.
We study the properties of an atom laser beam derived from a Bose-Einstein condensate using three different outcouplers, one based on multistate radio-frequency transitions and two others based on Raman transitions capable of imparting momentum to the beam. We first summarize the differences that arise in such systems, and how they may impact on the use of an atom laser in interferometry. Experimentally, we examine the formation of a bound state in all three outcouplers, a phenomenon which limits the atom laser flux, and find that a two-state Raman outcoupler is the preferred option for high-flux, low-divergence atom laser beams.
We describe our experimental setup for creating stable Bose–Einstein condensates (BECs) of 85Rb with tunable interparticle interactions. We use sympathetic cooling with 87Rb in two stages, initially in a tight Ioffe–Pritchard magnetic trap and subsequently in a weak, large-volume, crossed optical dipole trap, using the 155 G Feshbach resonance to manipulate the elastic and inelastic scattering properties of the 85Rb atoms. Typical 85Rb condensates contain 4×104 4 × 104 atoms with a scattering length of a = +200a0. Many aspects of the design presented here could be adapted to other dual-species BEC machines, including those involving degenerate Fermi–Bose mixtures. Our minimalist apparatus is well suited to experiments on dual-species and spinor Rb condensates, and has several simplifications over the 85Rb BEC machine at JILA, which we discuss at the end of this article.
We report on measurements of inelastic loss processes in ultracold 85Rb |F=2⟩ atoms. Our apparatus creates ultracold 85Rb clouds by sympathetic cooling with a 87Rb reservoir in a quadrupole-Ioffe magnetic trap and subsequently in a weak, large-volume optical dipole trap. We demonstrate strong sympathetic cooling of 85Rb in the magnetic trap, increasing its phase-space density by three orders of magnitude with no detectable loss in number. Ultracold samples created in this way are used to observe the variation of inelastic loss in 85Rb |F=2,mF=−2⟩ clouds as a function of magnetic field near the 155-G Feshbach resonance and to measure the decay due to inelastic losses in all five Zeeman sublevels of the F=2 manifold, finding a particularly high three-body recombination rate in the lowest energy state. We have also observed and characterized a previously unobserved loss feature at 219.9(1) G with a width of 0.28(6)G, which we associate with a narrow Feshbach resonance predicted by theory.