We present a protocol for generating nonclassical states of atomic spin ensembles through the backaction induced by a hybrid measurement of light that is entangled with atoms, combining both homodyne and single photon detection. In phase-I of the protocol we create a spin squeezed state by measuring the light's polarization rotation due to the Faraday effect in a balanced polarimeter, equivalent to a homodyne measurement. In phase-II we send a second probe beam through the sample and detect single photons scattered into the signal mode. Before doing so, we rotate the uncertainty bubble to increase the projection fluctuations of the measured spin component. This increases the coupling strength between the atoms and photons and thus the rate of scattering of single photons into the signal mode. In the ideal case, the result is a squeezed Dicke state, with substantial quantum advantage for sensing spin rotations. We benchmark the protocol's utility in the presence of inevitable decoherence due to optical pumping using the Fisher information as a measure of quantum advantage. We show that in the presence of decoherence, the quantum Fisher information associated with the nonGaussian mixed state we prepare is substantially larger than the classical Fisher information obtained from the standard measurement of spin rotations. We deduce a measurement basis that is close to optimal for achieving the quantum Cramér Rao bound in the presence of decoherence.
We present a protocol for generating nonclassical states of atomic spin ensembles through the backaction induced by a hybrid measurement of light that is entangled with atoms, combining both homodyne and single photon detection. In phase-I of the protocol we create a spin squeezed state by measuring the light's polarization rotation due to the Faraday effect in a balanced polarimeter, equivalent to a homodyne measurement. In phase-II we send a second probe beam through the sample and detect single photons scattered into the signal mode. Before doing so, we rotate the uncertainty bubble to increase the projection fluctuations of the measured spin component. This increases the coupling strength between the atoms and photons and thus the rate of scattering of single photons into the signal mode. In the ideal case, the result is a squeezed Dicke state, with substantial quantum advantage for sensing spin rotations. We benchmark the protocol's utility in the presence of inevitable decoherence due to optical pumping using the Fisher information as a measure of quantum advantage. We show that in the presence of decoherence, the quantum Fisher information associated with the nonGaussian mixed state we prepare is substantially larger than the classical Fisher information obtained from the standard measurement of spin rotations. We deduce a measurement basis that is close to optimal for achieving the quantum Cramér Rao bound in the presence of decoherence.
We present a protocol for generating nonclassical states of atomic spin ensembles through the backaction induced by a hybrid measurement of light that is entangled with atoms, combining both homodyne and single-photon detection. In phase I of the protocol we create a spin-squeezed state by measuring the light's polarization rotation due to the Faraday effect in a balanced polarimeter, equivalent to a homodyne measurement. In phase II we send a second probe beam through the sample and detect single photons scattered into the signal mode. Before doing so, we rotate the uncertainty bubble to increase the projection fluctuations of the measured spin component. This increases the coupling strength between the atoms and photons and thus the rate of scattering of single photons into the signal mode. In the ideal case, the result is a squeezed Dicke state, with substantial quantum advantage for sensing spin rotations. We benchmark the protocol's utility in the presence of inevitable decoherence due to optical pumping using the Fisher information as a measure of quantum advantage. We show that in the presence of decoherence, the quantum Fisher information associated with the non-Gaussian mixed state we prepare is substantially larger than the classical Fisher information obtained from the standard measurement of spin rotations. We deduce a measurement basis that is close to optimal for achieving the quantum Cram\'er-Rao bound in the presence of decoherence.
Abstract The quantum spin states of an atomic ensemble are of special interest to both fundamental studies and precision measurement applications. Here, we propose a scheme to prepare collective quantum states of an atomic ensemble placed in an optical cavity via homodyne measurement of a probing light field. The effective interactions of atoms mediated by photons are enhanced by the optical cavity, and the output probe light could also be entangled with the collective spin states. By selectively measuring the quadrature of the output light, we can prepare various quantum states, including superposition states of Dicke states and Dicke squeezed states. It is also demonstrated that the fidelity of the prepared quantum state can be enhanced by repetitive homodyne detection and using longer probe laser pulses. With the experimental parameters, we discuss some imperfections, including background noise, fluctuation of the measurement outcomes, and free-space scattering.We believe that our scheme should be feasible for experimental realization with current technologies, which may be used in the future study of quantum mechanics and quantum metrology.
Quantum control of many body atomic spins is often pursued in the context of an atom-light quantum interface, where a quantized light field acts as a "quantum bus" that can be used to entangle distant atoms. One key challenge is to improve the coherence of the atom-light interface and the amount of atom-light entanglement it can generate, given the constraints of working with multilevel atoms and optical fields in a 3D geometry. We have explored new ways to achieve this, through rigorous optimization of the spatial geometry, and through control of the internal atomic state. Our basic setup consists of a quantized probe beam passing through an atom cloud held in a dipole trap, first generating spin-probe entanglement through the Faraday interaction, and then using backaction from a measurement of the probe polarization to squeeze the collective atomic spin. The relevant figure of merit is the metrologically useful spin squeezing determined by the enhancement in the resolution of rotations of the collective spin, relative to the commonly used spin coherent state. With an optimized free-space geometry, and by using a 2-color probe scheme to suppress tensor light shifts, we achieve 3(2) dB of metrologically useful spin squeezing. We can further increase atom-light coupling by implementing internal state control to prepare spin states with larger initial projection noise relative to the spin coherent state. Under the right conditions this increase in projection noise can lead to stronger measurement backaction and increased atom-atom entanglement. With further internal state control the increased atom-atom entanglement can then be mapped to a basis where it corresponds to improved squeezing of, e.g., the physical spin-angular momentum or the collective atomic clock pseudospin. In practice, controlling the collective spin of N ~ 10⁶ atoms in this fashion is an extraordinarily difficult challenge because errors in the control of individual atoms tend to be highly correlated. By employing precise internal state control, we have prepared and detected projection noise limited "cat" states (which have initial projection noise that is larger by a factor of 2f = 8 for Cs relative to the spin coherent state) and estimate that we can generate up to 6.0(5) dB of metrologically useful spin squeezing, demonstrating the advantage of using the internal atomic structure as a resource for ensemble control.
Ultra-cold atoms are highly sensitive to both inertial effects and electromagnetic fields, making atom interferometers excellent candidates for a variety of precision sensing applications. Furthermore, highly tunable atomic interactions combined with well established experimental techniques for trapping, cooling and manipulating ensembles of ultra-cold atoms, make them well suited to quantum enhancement. For these reasons, ensembles of ultra-cold atoms are excellent candidates for quantum-enhanced measurement devices. Broadly, this thesis presents a number of theoretical results which share the aim of progressing the proof-of-principle regime of current experiments to genuinely useful, ultra-precise quantum enhanced sensors.In Chapter 4 we explore the challenge of devising a useful, quantum-enhanced inertial measurement - to date no such experiment has been performed. Specifically, we present a model of a spin-squeezed rotation sensor utilising the Sagnac effect in a spin-1 Bose-Einstein condensate in a ring trap. The two input states for the interferometer are seeded using Raman pulses with Laguerre-Gauss beams and are amplified by the bosonic enhancement of spin-exchange collisions, resulting in spin-squeezing and potential quantum enhancement in the interferometry. The ring geometry has an advantage over separated beam path atomic rotation sensors due to the uniform condensate density. We model the interferometer both analytically and numerically for realistic experimental parameters and find that significant quantum enhancement is possible. However, this enhancement is partially degraded when working in a regime with strong atomic interactions, indicating that perhaps interaction-based squeezing is not the best route to a quantum-enhanced inertial measurement.Continuing the theme of practical spin-squeezing with atomic interactions, in Chapter 5 we explore methods to combat detection noise, which is currently one of the most significant experimental limitations for quantum-enhanced atom interferometers. A useful quantum-enhanced interferometer requires nonclassical states with a high particle number and the (close to) optimal exploitation of the states' quantum correlations. Unfortunately, the single-particle detection resolution demanded by conventional protocols, such as spin squeezing via one-axis twisting, places severe limits on the particle number. Additionally, the challenge of finding optimal measurements (that saturate the quantum Cram´er-Rao bound) for an arbitrary nonclassical state limits most metrological protocols to only moderate levels of quantum enhancement. “Interaction-based readout” protocols have been shown to allow optimal interferometry or to provide robustness against detection noise at the expense of optimality. We prove that one has great flexibility in constructing an optimal protocol, thereby allowing it to also be robust to detection noise. This requires the full probability distribution of outcomes in an optimal measurement basis, which is typically easily-accessible and can be determined from specific criteria we provide. Additionally, we quantify the robustness of several classes of interaction-based readouts under realistic experimental constraints. We determine that optimal and robust quantum metrology is achievable in current spin-squeezing experiments.Macroscopic superposition states (known as spin-cat states in atomic ensembles) achieve the ultimate quantum precision limit. In Chapters 6 and 7 we turn our attention to studying decoherence that arises in creating and manipulating these states. In its simplest form, decoherence occurs when a quantum state is entangled with a second state, but the results of measurements made on the second state are not accessible. As the second state has effectively ``measured the first, in Chapter 6 we argue that the quantum Fisher information is the relevant metric for predicting and quantifying this kind of decoherence. In particular we apply this analysis to studying decoherence imparted on spin-cat states via atom-light interactions, which are an essential process in atom interferometry. We find that, compared to classical atomic states, spin-cat states are highly susceptible to this kind of decoherence. We investigate the required optical field occupation, such that this decoherence is negligible.Finally, in Chapter 7 we explore the deleterious effects of spatial and phase dynamics during the creation of spin-cat states via one-axis twisting in a two-component Bose-Einstein condensate. We simulate the breathing dynamics in 1 spatial dimension, employing the method of Sinatra and Castin, whereby the state is expanded into the Fock basis, with each basis state evolving within the Hartree-Fock approximation. This method is able to capture both multi-mode effects and quantum correlations, which allows us to calculate the quantum Fisher information. We find that so long as the time taken for the condensate to reach a spin-cat state is an integer multiple of the breathing period, it is sometimes possible to realise something extremely close to a spin-cat state, despite significant dynamics. These results indicate that large non-linearities, and the associated speed-up in entangling dynamics, are not fundamentally incompatible with the production of fragile, highly entangled states such as spin-cat states.
We study the three-dimensional nature of the quantum interface between an ensemble of cold, trapped atomic spins and a paraxial laser beam, coupled through a dispersive interaction. To achieve strong entanglement between the collective atomic spin and the photons, one must match the spatial mode of the collective radiation of the ensemble with the mode of the laser beam while minimizing the effects of decoherence due to optical pumping. For ensembles coupling to a probe field that varies over the extent of the cloud, the set of atoms that indistinguishably radiates into a desired mode of the field defines an inhomogeneous spin wave. Strong coupling of a spin wave to the probe mode is not characterized by a single parameter, the optical density, but by a collection of different effective atom numbers that characterize the coherence and decoherence of the system. To model the dynamics of the system, we develop a full stochastic master equation, including coherent collective scattering into paraxial modes, decoherence by local inhomogeneous diffuse scattering, and backaction due to continuous measurement of the light entangled with the spin waves. This formalism is used to study the squeezing of a spin wave via continuous quantum nondemolition (QND) measurement. We find that the greatest squeezing occurs in parameter regimes where spatial inhomogeneities are significant, far from the limit in which the interface is well approximated by a one-dimensional, homogeneous model.
Remote state preparation is a fundamental quantum-information protocol that exploits prior knowledge of a target state to reduce the communication resources required for quantum-state distribution. Here, we propose a remote-state-preparation protocol for a stationary electron-spin qubit using hybrid entanglement between the electron spin and a coherent-state light pulse, generated by spin-dependent reflection from a spin-cavity system. Unlike single-photon encodings, the coherent-state encoding is naturally tolerant of photon loss: a loss channel attenuates the coherent-state amplitude, leading to a gradual reduction in preparation fidelity rather than probabilistic protocol failure. The central difficulty---implementing the projection onto superpositions of nonorthogonal coherent states required in the conventional protocol---is circumvented by coupling the transmitted pulse to an auxiliary spin, followed by homodyne detection and a spin projective measurement. The protocol therefore avoids direct coherent-state-superposition measurements and photon-number-resolving detection. In the ideal limit, deterministic preparation of a particular class of target states can be achieved using only one bit of classical communication. We analytically quantify the effects of coherent-state nonorthogonality, fiber loss, and spin dephasing on the preparation fidelity. Increasing the coherent-state amplitude improves state distinguishability and hence the preparation fidelity, but also enhances which-branch information leakage caused by photon loss, resulting in an optimal amplitude at each transmission distance. For experimentally relevant parameters, the optimized average fidelity remains well above the classical benchmark over distances of tens of kilometers. We also discuss a possible implementation using diamond nitrogen-vacancy centers.