The primary study of this thesis is spin-nematic squeezing in a spin-1 condensate. \nThe measurement of spin-nematic squeezing builds on the success of previous experiments of spin-mixing together with advances in low noise atom counting. \nThe major contributions of this thesis are linking theoretical models to experimental results and the development of the intuition and tools to address the squeezed subspaces. \nUnderstanding how spin-nematic squeezing is generated and how to measure it has required a review of several theoretical models of spin-mixing as well as extending these existing models. This extension reveals that the squeezing is between quadratures of a spin moment and a nematic (quadrapole) moment in abstract subspaces of the SU(3) symmetry group of the spin-1 system. \nThe identification of the subspaces within the SU(3) symmetry allowed the development of techniques using RF and microwave oscillating magnetic fields to manipulate the phase space in order to measure the spin-nematic squeezing. Spin-mixing from a classically meta-stable state, the phase space manipulation, and low noise atom counting form the core of the experiment to measure spin-nematic squeezing. Spin-nematic squeezing is also compared to its quantum optics analogue, two-mode squeezing generated by four-wave mixing. \n \nThe other experimental study in this thesis is performing spin-dependent photo-association spectroscopy. Spin-mixing is known to depend on the difference of the strengths of the scattering channels of the atoms. Optical Feshbach resonances have been shown to be able to alter these scattering lengths but with prohibitive losses of atoms near the resonance. The possibility of using multiple nearby resonances from different scattering channels has been proposed to overcome this limitation. However there was no spectroscopy in the literature which analyzes for the different scattering channels of atoms for the same initial states. Through analysis of the initial atomic states, this thesis studies how the spin state of the atoms affects what photo-association resonances are available to the colliding atoms based on their scattering channel and how this affects the optical Feshbach resonances. From this analysis a prediction is made for the extent of alteration of spin-mixing achievable as well as the impact on the atom loss rate.
The primary study of this thesis is spin-nematic squeezing in a spin-1 condensate. \nThe measurement of spin-nematic squeezing builds on the success of previous experiments of spin-mixing together with advances in low noise atom counting. \nThe major contributions of this thesis are linking theoretical models to experimental results and the development of the intuition and tools to address the squeezed subspaces. \nUnderstanding how spin-nematic squeezing is generated and how to measure it has required a review of several theoretical models of spin-mixing as well as extending these existing models. This extension reveals that the squeezing is between quadratures of a spin moment and a nematic (quadrapole) moment in abstract subspaces of the SU(3) symmetry group of the spin-1 system. \nThe identification of the subspaces within the SU(3) symmetry allowed the development of techniques using RF and microwave oscillating magnetic fields to manipulate the phase space in order to measure the spin-nematic squeezing. Spin-mixing from a classically meta-stable state, the phase space manipulation, and low noise atom counting form the core of the experiment to measure spin-nematic squeezing. Spin-nematic squeezing is also compared to its quantum optics analogue, two-mode squeezing generated by four-wave mixing. \n \nThe other experimental study in this thesis is performing spin-dependent photo-association spectroscopy. Spin-mixing is known to depend on the difference of the strengths of the scattering channels of the atoms. Optical Feshbach resonances have been shown to be able to alter these scattering lengths but with prohibitive losses of atoms near the resonance. The possibility of using multiple nearby resonances from different scattering channels has been proposed to overcome this limitation. However there was no spectroscopy in the literature which analyzes for the different scattering channels of atoms for the same initial states. Through analysis of the initial atomic states, this thesis studies how the spin state of the atoms affects what photo-association resonances are available to the colliding atoms based on their scattering channel and how this affects the optical Feshbach resonances. From this analysis a prediction is made for the extent of alteration of spin-mixing achievable as well as the impact on the atom loss rate.
Exotic types of magnetic order and phases resulting from collective behaviour of quantum spins are an important focus of many-body physics. Nematic or quadrupolar ordering of spins is one such example [1], which breaks O(3) rotational symmetry, has no magnetic moment and is analogous to the well-known ordering of molecules in nematic phases of liquid crystals [2]. Spin nematic phases have been posited for a variety of condensed matter systems including frustrated quantum magnets [3–5], and heavyfermion [6] and iron-based superconductors [7], although they are challenging to detect directly [8]. Spin-1 atomic Bose-Einstein condensates [9– 11] provide a natural system to investigate spinnematic quantum phases with a key advantage that the nematic tensor is directly measurable. Here, we measure spin-nematic fluctuations in a spin-1 condensate following a quench through a nematic to ferromagnetic quantum phase transition and observe quadrature squeezing in the variance of the fluctuations up to −8.3 −0.7 dB (−10.3 −0.9 dB corrected for detection noise) below the standard quantum limit. Previous work in atomic squeezing has employed two-level systems exhibiting SU(2) symmetry on the Bloch sphere [12, 13], while the squeezing observed here is an example of squeezing in an SU(3) system. These results demonstrate spin-nematic dynamics in the quantum regime and could form the basis of a quantum-enhanced magnetometer.
Investigations of spin squeezing in ensembles of quantum particles have been limited primarily to a subspace of spin fluctuations and a single spatial mode in high-spin and spatially extended ensembles. Here, we show that a wider range of spin squeezing is attainable in ensembles of high-spin atoms, characterized by sub-quantum-limited fluctuations in several independent planes of spin-fluctuation observables. Further, considering the quantum dynamics of an f =1 ferromagnetic spinor Bose–Einstein condensate, we demonstrate theoretically that a high degree of spin squeezing is attained in multiple spatial modes of a spatially extended quantum field and that such squeezing can be extracted from spatially resolved measurements of magnetization and nematicity, i.e. the vector and quadrupole magnetic moments, of the quantum gas. Taking into account several experimental limitations, we predict that the variance of the atomic magnetization and nematicity may be reduced as far as 20 dB below the standard quantum limits.
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.
The quantum properties of matter waves, in particular quantum correlations and entanglement are an important frontier in atom optics with applications in quantum metrology and quantum information. In this thesis, we report the first observation of sub-Poissonian fluctuations in the magnetization of a spinor 87Rb condensate. The fluctuations in the magnetization are reduced up to 10 dB below the classical shot noise limit. This relative number squeezing is indicative of the predicted pair-correlations in a spinor condensate and lay the foundation for future experiments involving spin-squeezing and entanglement measurements. We have investigated the limits of the imaging techniques used in our lab, absorption and fluorescence imaging, and have developed the capability to measure atoms numbers with an uncertainly < 10 atoms. Condensates as small as ≈ 10 atoms were imaged and the measured fluctuations agree well with the theoretical predictions. Furthermore, we implement a reliable calibration method of our imaging system based on quantum projection noise measurements. We have resolved the individual lattice sites of a standing-wave potential created by a CO2 laser, which has a lattice spacing of 5.3 µm. Using microwaves, we site-selectively address and manipulate the condensate and therefore demonstrate the ability to perturb the lattice condensate of a local level. Interference between condensates in adjacent lattice sites and lattice sites separated by a lattice site are observed.
Abstract We propose a simple scheme to realize the persistent spin-nematic squeezing in a spinor Bose–Einstein condensate by rapidly turning-off the external magnetic field at a time that maximal spin-nematic squeezing occurs. We observe that the optimal spin-nematic squeezing can be maintained in a nearly fixed direction. For a proper initial magnetic field, the optimal squeezing can be obviously enhanced. We further construct a spin-mixing interferometer, where the quantum correlation of the squeezed state (generated by our scheme) is fully utilized in the phase measurement, and show the phase sensitivity of the interferometer has a significant enhancement.
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.