The generation of entanglement in atomic systems plays a central topic in the fields of quantum information storage and processing. Moreover, a special category of entangled states of multi-atom ensembles, spin squeezed states, have been proven to lead to considerable improvement in the sensitivity of precision measurements compared to systems involving uncorrelated atoms. A treatment of entanglement in open systems is, however, incomplete without a precise description of the process of decoherence which necessarily accompanies it. The theory of entanglement and decoherence are the two main topics of this thesis. Methods are described for the generation of strong correlations in large atomic ensembles using either cavity quantum electrodynamics or measurement outcome conditioned quantum dynamics. Moreover, the description of loss of entanglement resulting from the coupling to a noise reservoir (electromagnetic vacuum) is explored. A spin squeezing parameter is used throughout this thesis as both a measure of entanglement strength and as an indication of the sensitivity improvement above the so-called standard quantum limit (sensitivity obtained with uncorrelated particles) in metrology. The first scheme considered consists of a single mode cavity field interacting with a collection of atoms for which spin squeezing is produced in both resonant and off-resonant regimes. In the resonant case, transfer of squeezing from a field state to the atoms is analyzed, while in the off-resonant regime squeezing is produced via an effective nonlinear interaction (one-axis twisting Hamiltonian). A second, more experimentally realistic case, is one involving the interaction of free space atoms with laser pulses; a projective measurement of a source field originating from atomic fluctuations provides a means of preparing atomic collective states such as spin squeezed and Schrodinger cat states. A new unravelling is proposed, that employs the detection of photon number in a single output channel and is capable of producing mesoscopic Schrodinger cat states in a single step. As a first step to understanding the role of cooperative decoherence, of importance in the case of dense pencil-shaped atomic ensembles, the collective spin decoherence of a two multilevel atom system is derived. This calculation is also relevant to entanglement loss for two qubits manipulated using with reading/writing pulses. Finally, a scheme is proposed in which arbitrarily strong entanglement can be produced in a four-wave mixing setup, where the preparation of the atoms in a dark state limits the decoherence to negligible values.
The generation of entanglement in atomic systems plays a central topic in the fields of quantum information storage and processing. Moreover, a special category of entangled states of multi-atom ensembles, spin squeezed states, have been proven to lead to considerable improvement in the sensitivity of precision measurements compared to systems involving uncorrelated atoms. A treatment of entanglement in open systems is, however, incomplete without a precise description of the process of decoherence which necessarily accompanies it. The theory of entanglement and decoherence are the two main topics of this thesis. Methods are described for the generation of strong correlations in large atomic ensembles using either cavity quantum electrodynamics or measurement outcome conditioned quantum dynamics. Moreover, the description of loss of entanglement resulting from the coupling to a noise reservoir (electromagnetic vacuum) is explored. A spin squeezing parameter is used throughout this thesis as both a measure of entanglement strength and as an indication of the sensitivity improvement above the so-called standard quantum limit (sensitivity obtained with uncorrelated particles) in metrology. The first scheme considered consists of a single mode cavity field interacting with a collection of atoms for which spin squeezing is produced in both resonant and off-resonant regimes. In the resonant case, transfer of squeezing from a field state to the atoms is analyzed, while in the off-resonant regime squeezing is produced via an effective nonlinear interaction (one-axis twisting Hamiltonian). A second, more experimentally realistic case, is one involving the interaction of free space atoms with laser pulses; a projective measurement of a source field originating from atomic fluctuations provides a means of preparing atomic collective states such as spin squeezed and Schrodinger cat states. A new unravelling is proposed, that employs the detection of photon number in a single output channel and is capable of producing mesoscopic Schrodinger cat states in a single step. As a first step to understanding the role of cooperative decoherence, of importance in the case of dense pencil-shaped atomic ensembles, the collective spin decoherence of a two multilevel atom system is derived. This calculation is also relevant to entanglement loss for two qubits manipulated using with reading/writing pulses. Finally, a scheme is proposed in which arbitrarily strong entanglement can be produced in a four-wave mixing setup, where the preparation of the atoms in a dark state limits the decoherence to negligible values.
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.
In this thesis I explore the use of collective spin angular momentum as a platform for quantum information processing. Such systems have several nice features that make them excellent choices for such protocols, especially ones where information is also stored in photonic variables. The longer coherence times of atoms makes it possible to store information from light in atoms for future use, and it is generally easier to couple atomic variables than to create nonlinear interactions of light. Above and beyond the advantages of atomic systems, collective atomic systems have additional strengths. In the limit of a large number of atoms, the collective variables of atomic systems have a natural connection to the bosonic algebra of light (known as the Holstein-Primakoff or HP approximation) where components of the collective spin angular momentum effectively act as quadratures, making them natural systems for coupling to light. Also, collectively addressing the atoms allows one to access a large state space without individual addressing of the atoms. A natural first step towards control of these collective variables is generating large amounts of atomic spin squeezing. In the HP approximation going from rotations to squeezing corresponds to going from linear to quadratic interactions in the atomic quadratures; for extremely large squeezing one should see the breakdown of the HP approximation and the ability to generate arbitrary collective atomic states. I have sought to improve previous schemes for the spin squeezing of atomic ensembles, such as the proposal of Takeuchi et. al. based on coherent quantum feedback. In this scheme a beam of linearly polarized light passes through the atomic ensemble (prepared in a coherent state), coupling to the atoms through a state-dependent index of refraction (the Faraday effect). The light is then passed through a wave-plate and reflected back through the atoms for a second pass. This double-pass scheme leads to an effective nonlinearity as the atomic fluctuations are mapped onto the light on the first pass and then back on to the atoms in the second pass. The light acts as a bus coupling each atom to each of the others. This nonlinear interaction forms a shearing of the atomic coherent state that results in squeezing. The light is entangled to the atoms through these interactions, and remains entangled as it escapes the system. This leads to decoherence of the atoms as the light is lost to the environment, reducing the amount of spin squeezing achieved. The first step towards improving the double-pass scheme was to add a quantum eraser step in which the light is disentangled from the squeezed atoms. By first measuring one quadrature of the light, and then performing a measurement-dependent rotation on the atomic ensemble, it is possible to decouple the atoms and light so that the loss of the light does not reduce the atomic squeezing. This results in an improvement of the rate of atomic spin squeezing. The nonlinear shearing interaction that remains still falls short of the exponential squeezing seen in optical parametric amplification. The reason for this can be seen by decomposing the shearing interaction into squeezing along a given quadrature followed by a rotation. The rotation leads to a constantly changing axis along which the squeezing occurs, and thus the squeezing builds up more slowly. This can be corrected for by breaking up the light pulse into a sequence of small pulses, and performing a small phase matching rotation after each pulse. The squeezing then adds up along a constant direction, rather than along a constantly varying direction. This results in still further improvement of the rate of atomic spin squeezing. A complete model includes the effects of photon-atom scattering and other noise and loss effects on the overall rate of squeezing. Previous derivations of noise due to photon-atom scattering have started with the unjustified assumptions that the atomic and photonic decoherence channels were both Gaussian and independent of correlations between the two subsystems. They then proceed with very general statistical arguments that rely upon these simplifications. My work begins with the more fundamental master equation picture in which I find the Linblad jump operators. I find that in general the photonic and atomic loss channels are not independent, with the intensity of the light dictating the details of this dependence, and find the conditions under which the Gaussian approximation holds. Squeezing and loss is initially treated assuming ensembles of spin-1/2 atoms, but this work is further extended to higher dimensional subsystems. For a higher spin case, preparing the atoms in spin coherent states is not optimal. One can engineer a stronger interaction by preparing the atoms in an atomic "cat state", i.e., a superposition of the two stretch states along the direction of propagation of the light beam. The fluctuations of such a state are more strongly coupled to the light, resulting in a stronger nonlinearity. This leads to strong correlations between the atoms, but they are not immediately useful for squeezing; the cat state must be coherently mapped to a coherent state to achieve atomic spin squeezing. The state created in this manner is ultimately more squeezed than that achieved with the same interaction but prepared initially in a coherent state.
After they have interacted, quantum particles generally behave as a single nonseparable entangled system. The concept of entanglement plays an essential role in quantum physics. We have performed entanglement experiments with Rydberg atoms and microwave photons in a cavity and tested quantum mechanics in situations of increasing complexity. Entanglement resulted either from a resonant exchange of energy between atoms and the cavity field or from dispersive energy shifts affecting atoms and photons when they were not resonant. With two entangled particles (two atoms or one atom and a photon), we have realized new versions of the Einstein-Podolsky-Rosen situation. The detection of one particle projected the other, at a distance, in a correlated state. This process could be viewed as an elementary measurement, one particle being a ``meter'' measuring the other. We have performed a ``quantum nondemolition'' measurement of a single photon, which we detected repeatedly without destroying it. Entanglement is also essential to understand decoherence, the process accounting for the classical appearance of the macroscopic world. A mesoscopic superposition of states (``Schr\"odinger cat'') gets rapidly entangled with its environment, losing its quantum coherence. We have prepared a Schr\"odinger cat made of a few photons and studied the dynamics of its decoherence, in an experiment which constitutes a glimpse at the quantum/classical boundary. We have also investigated entanglement as a resource for the processing of quantum information. By using quantum two-state systems (qubits) instead of classical bits of information, one can perform logical operations exploiting quantum interferences and taking advantage of the properties of entanglement. Manipulating as qubits atoms and photons in a cavity, we have operated a quantum gate and applied it to the generation of a complex three-particle entangled state. We finally discuss the perspectives opened by these experiments for further fundamental studies.
In most proposals for the generation of entanglement in large ensembles of atoms via projective measurements, the interaction with the vacuum is responsible for both the generation of the signal that is detected and the spin depolarization or decoherence. In consequence, one must usually work in a regime where the information acquisition via detection is sufficiently slow (weak measurement regime) such as not to strongly disturb the system. We propose here a four-wave mixing scheme where, owing to the pumping of the atomic system into a dark state, the polarization of the ensemble is not critically affected by spontaneous emission. In the language of spin squeezing, the removal of the limitations imposed by spontaneous emission allows one to work in a strong signal regime where the Heisenberg limit can be reached.
Large ensembles of uncorrelated atoms are extensively used as precise sensors of time, rotation, and gravity, and for tests of fundamental physics. The quantum nature of the sensors imposes a limit on their ultimate precision. Larger ensembles of N atoms can be used to average the quantum noise as 1/√N, a scaling known as the standard quantum limit. However, the ensemble size may be limited by technical constraints and/or atom-atom collisions -- a fundamental distinction from photon-based sensors. Learning to prepare entangled states of large ensembles with noise properties below the standard quantum limit will be key to extending both the precision and/or bandwidth of atomic sensors. More broadly, the generation and application of entanglement to solve problems is a core goal of quantum information science being pursued in both atomic and solid state systems.\nIn this thesis, we utilize the tools of cavity-QED to prepare entangled spin-squeezed states with 3.4(6) dB improvement in spectroscopic sensitivity over the standard quantum limit. The collective atomic spin is composed of the two-level clock states of 87Rb confined in a medium finesse F = 710 optical cavity. We employ cavity-aided quantum non-demolition measurements of the vacuum Rabi splitting to measure and subtract out the quantum projection noise of the collective spin state, preparing states with collective atomic spin projection noise 4.9(6) dB below the projection noise level. The conditionally reduced spin noise combined with the measured 1.5(3) dB reduction in the mean spin length implies a net 3.4(6) dB spectroscopic enhancement or conditional squeezing as defined by the Wineland criterion. Our method does not require single particle addressability and is applied to a spectroscopically large ensemble of N = 7 x 105 atoms using two collective population measurements, with the whole squeezing operation taking ~ 150 μs. The gain in sensitivity is spectroscopically equivalent to the enhancement obtained had we created > 105 pairs of maximally entangled qubits, demonstrating the power of a top-down approach for entangling large ensembles. The nondemolition probing of atomic populations via the vacuum Rabi splitting is also of broad interest for non-destructively reading out a wide variety of both atomic and solid state qubits.
In an ensemble of two-level atoms that can be described in terms of a collective spin, entangled states can be used to enhance the sensitivity of interferometric precision measurements. While non-Gaussian spin states can produce larger quantum enhancements than spin-squeezed Gaussian states, their use requires the measurement of observables that are nonlinear functions of the three components of the collective spin. In this paper we develop strategies that achieve the optimal quantum enhancements using non-Gaussian states produced by a nonlinear one-axis-twisting Hamiltonian, and show that measurement-after-interaction techniques, known to amplify the output signals in quantum parameter estimation protocols, are effective in measuring nonlinear spin observables. Including the presence of the relevant decoherence processes from atomic experiments, we determine analytically the quantum enhancement of non-Gaussian over-squeezed states as a function of the noise parameters for arbitrary atom numbers.