We describe an experiment where spin squeezing occurs spontaneously within a standard Ramsey sequence driving a two-component Bose–Einstein condensate (BEC) of 87 Rb atoms trapped in an elongated magnetic trap. The squeezing is generated by state-dependent collisional interactions, despite the near-identical scattering lengths of the spin states in 87 Rb. In our proof-of-principle experiment, we observe a metrological spin squeezing that reaches 1.3 ± 0.4 dB for 5000 atoms, with a contrast of 90 ± 1%. The method may be applied to realize spin-squeezed BEC sources for atom interferometry without the need for cavities, state-dependent potentials or Feshbach resonances.
We describe an experiment where spin squeezing occurs spontaneously within a standard Ramsey sequence driving a two-component Bose–Einstein condensate (BEC) of 87 Rb atoms trapped in an elongated magnetic trap. The squeezing is generated by state-dependent collisional interactions, despite the near-identical scattering lengths of the spin states in 87 Rb. In our proof-of-principle experiment, we observe a metrological spin squeezing that reaches 1.3 ± 0.4 dB for 5000 atoms, with a contrast of 90 ± 1%. The method may be applied to realize spin-squeezed BEC sources for atom interferometry without the need for cavities, state-dependent potentials or Feshbach resonances.
We study the evolution of a Bose–Einstein condensate in a two-state superposition due to inter-state interactions. Using a population imbalanced dynamic decoupling scheme, we measure inter-state interactions while canceling intra-state density shifts and external noise sources. Our measurements show low statistical uncertainties for both magnetic sensitive and insensitive superpositions, indicating that we successfully decoupled our system from strong magnetic noises. We experimentally show that the Bloch sphere representing general superposition states is 'twisted' by inter-state interactions, as predicted in [ 1 , 2 ] and the twist rate depends on the difference between inter-state and intra-state scattering lengths a 22 + a 11 − 2 a 12 . We use the non-linear spin dynamics to demonstrate squeezing of Gaussian noise, showing 2.79 ± 0.43 dB squeezing when starting with a noisy state and applying 160 echo pulses, which can be used to increase sensitivity when there are errors in state preparation. Our results allow for a better understanding of inter-atomic potentials in 87 Rb. Our scheme can be used for spin-squeezing beyond the standard quantum limit and observing polaron physics close to Feshbach resonances, where interactions diverge, and strong magnetic noises are ever present.
We theoretically investigate the creation of squeezed states of a Bose-Einstein condensate (BEC) trapped in a magnetic double-well potential. The number or phase squeezed states are created by modulating the tunnel coupling between the two wells periodically with twice the Josephson frequency, i.e., through parametric amplification. Simulations are performed with the multiconfigurational time-dependent Hartree method for bosons. We employ optimal control theory to bring the condensate to a complete halt at a final time, thus creating a highly squeezed state (squeezing factor of 0.12, ${\ensuremath{\xi}}_{S}^{2}=\ensuremath{-}18$ dB) suitable for atom interferometry.
In recent years, atom interferometry has become established as an indispensable tool in both fundamental and applied physics. With present state-of-the-art devices based on thermal atoms reaching limits imposed by the momentum spread of the initial atomic wavepacket, it seems natural to ask whether colder sources such as Bose-Einstein condensates may prove beneficial in advancing the precision of interferometric measurements. The thesis at hand aims to inform this question, specifically by examining the role played by atomic interactions in interferometers based on Bose-condensed atoms. Interactions can have both advantageous and deleterious consequences in the context of atom interferometry. They provide a means to control the momentum width of the condensate, and facilitate the generation of nonclassical squeezed states which may enhance the phase sensitivity beyond the shot noise limit. Conversely, the condensate self-interaction causes mean-field shifts, multimode excitations and phase diffusion which can erode both the precision and the accuracy of an interferometric measurement. The question of when and in which systems the detrimental effects of interactions outweigh the advantages of using Bose-Einstein condensates is an important one, and warrants investigation. This thesis presents experimental studies into the role of interactions in both internal- and external-state atom interferometers. As a foundation for these investigations, we describe the design and construction of an apparatus for creating Bose-Einstein condensates of the two stable rubidium isotopes in an optical trap. By sympathetic cooling with a rubidium-87 reservoir, we are able to produce condensates of rubidium-85 in which the interactions may be adjusted by means of a magnetic Feshbach resonance. The tunability afforded by the Feshbach resonance is used to study inelastic losses in ultracold rubidium-85 clouds, as well as the effect of interactions on condensate stability and on the ground state of dual-species mixtures. In particular, we offer new experimental data on the dynamics of collapsing condensates with attractive interactions, over which some controversy has existed since the first experiments more than a decade ago. Good agreement is found between the measured collapse times and a simple mean-field model. Proceeding to interferometry, we present results from Ramsey interferometers operating on the clock transition of rubidium-87 Bose-Einstein condensates. In free-space operation with Raman beamsplitters, we demonstrate projection-noise-limited performance, an important prerequisite for the realisation of squeezing-enhanced sensitivity. Using large condensates of up to 10⁶ atoms and microwave coupling, we study the effect of interactions on the Ramsey fringe contrast. The dominant source of decoherence is found to be spatial dynamics driven by the difference in interparticle interaction strengths, which are analysed using the spin-echo technique and numerical simulations of the Gross-Pitaevskii equation. Finally, we turn our attention to external-state interferometry, implementing a Mach-Zehnder gravimeter using Bragg transitions in a freely falling rubidium-87 condensate. Large-momentum-transfer beamsplitters composed of higher-order Bragg diffraction and Bloch oscillations are used to increase the accumulated phase and thus the sensitivity of the interferometer. The role of interactions in this system is examined, and we canvass methods for achieving further increases in sensitivity.
This chapter describes the use of squeezed states to improve the sensitivity in the estimation of the relative phase accumulated in a Bose--Einstein condensate (BEC) beyond the standard quantum limit. We begin by examining the specific example of a two-component BEC, where atoms in two different hyperfine levels interact with each other. By evolving an initial superposition of states under an effective Hamiltonian, a squeezed state is realized. Next, the squeezing is visualized using the Q-function, giving the mean spin direction and shape of the BEC distribution. We discuss the basic operation of Ramsey interferometry, which is a classic example of two-slit atom diffraction. We then calculate the error in estimating the relative phase shift using the error propagation formula that allows us to define the squeezing parameter. This measures the amount of metrological gain using squeezed states over unsqueezed states. We give an example of the metrological gain in the estimation of the relative phase shift using a squeezed state of the two-component BEC as an input state to an atom Mach--Zehnder interferometer. The Fisher information is used to find which rotation axis gives the optimal information from a given initial state. Finally, we parameterize the nonlinear phase per atom responsible for squeezing and discuss how this parameter is controlled in different experiments.
We measure inter-state interactions in a Bose-Einstein Condensate (BEC) set in a superposition of two states, using microwave spectroscopy. We introduce a population imbalanced dynamic-decoupling scheme that accumulates a phase due to inter-state interactions while canceling intra-state density shifts and external noise sources. Uncertainties of the measured scattering lengths were 0.02a0 (where a0 is the Bohr radius) for both magnetic sensitive and insensitive transitions, indicating that we successfully decoupled our system from strong magnetic noises. We experimentally show that the Bloch sphere representing general superposition states is twisted by the nonlinear interactions, as predicted by Harber et. al and that the twist rate depends on the difference between inter-state and intra-state scattering lengths a22+a11−2a12. Our results allow for a better understanding of inter-atomic potentials in 87Rb. Our scheme can be used for spin squeezing and observing polaron physics close to a Feshbach resonance, where interactions diverge, and strong magnetic noises are ever present.
The controlled generation of entanglement forms the basis for currently emerging ‘quantum technologies’, such as quantum simulation, computation, and metrology. In the field of quantum metrology, multi-particle entangled states, such as spin-squeezed states, are investigated as a means to improve measurement precision beyond the ‘standard quantum limit’. This limit arises from the quantum noise inherent in measurements on a finite number of uncorrelated particles and limits today’s best atomic clocks. Atom chips combine exquisite coherent control of ultracold atoms with a compact and robust setup, suggesting their use for quantum metrology with portable atomic clocks and interferometers. A severe limitation of atom chips, however, is that techniques to control atomic interactions and to generate entanglement have not been experimentally available so far. In this thesis, I present experiments where we generate for the first time multi-particle entanglement on an atom chip. We achieve this by controlling elastic collisional interactions with a state-dependent potential. We employ this novel technique to generate spin-squeezed states of a two-component Bose-Einstein condensate and show that they are a useful resource for quantum metrology, as they could be used to improve an interferometric measurement by 2.5 dB over the standard quantum limit. The state-dependent potential is created with the help of a coplanar microwave guide, which is integrated on our atom chip. In the vicinity of this waveguide a microwave nearfield is formed. When a Bose-Einstein condensate of 87Rb is brought into this near-field, the hyperfine energy levels of the atoms are shifted differentially due to the AC Zeeman effect. The strong gradients in the field can be used to state-selectively shift the minimum of a static magnetic atom trap and thus coherently split an ensemble of atoms which have been prepared in a superposition of two internal states. During this process, nonlinear atomic interactions lead to the formation of a spinsqueezed state. I tomographically analyze the produced state, reconstruct its Wigner function, and deduce that it is at least four-particle entangled. I compare our results with a dynamical multi-mode simulation which takes not only the atomic motion and internal state dynamics but also particle losses into account and find good agreement. Moreover, I use this comparison to identify technical noise sources in our experiment, which currently limit the achieved amount of squeezing, and make suggestions on how to eliminate them in future experiments. Our method can in principle create a very large amount of squeezing and entanglement and is applicable to a wide variety of atomic systems, in particular to those for which no convenient Feshbach resonance exists. We envisage the implementation of this technique in portable atomic clocks and interferometers operating beyond the standard quantum limit. Furthermore, it is a valuable tool for experiments on many-body quantum physics and could enable quantum information processing on atom chips.