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We demonstrate quantum control of a large spin angular momentum associated with the F=3 hyperfine ground state of 133Cs. Time-dependent magnetic fields and a static tensor light shift are used to implement near-optimal controls and map a fiducial state to a broad range of target states, with yields in the range 0.8-0.9. Squeezed states are produced also by an adiabatic scheme that is more robust against errors. Universal control facilitates the encoding and manipulation of qubits and qudits in atomic ground states and may lead to the improvement of some precision measurements.

A weak continuous quantum measurement of an atomic spin ensemble can be implemented via Faraday rotation of an off-resonance probe beam, and may be used to create and probe nonclassical spin states and dynamics. We show that the probe light shift leads to nonlinearity in the spin dynamics and limits the useful Faraday measurement window. Removing the nonlinearity allows a non-perturbing measurement on the much longer timescale set by decoherence. The nonlinear spin Hamiltonian is of interest for studies of quantum chaos and real-time quantum state estimation.PACS numbers: 42.50. Ct, 03.65.Ta The process of quantum measurement involves a fundamental tradeoff between information gain and disturbance. In a projective measurement, this backaction is strong enough to collapse the state of the system and disrupt its coherent evolution. In more realistic scenarios, the system is weakly coupled to a probe, which is then measured to gain small amounts of information at the cost of modest perturbation. Continuous versions of this weak measurement scheme are of particular interest in the context of real-time feedback control and the creation and probing of non-classical states and dynamics [1]. Generally, the coupling of a probe to a single quantum system is so weak that the signal carrying information about the system becomes masked by probe noise. The signal-to-noise ratio of the measurement can be improved by coupling the probe to an ensemble of identically prepared systems, while at the same time the backaction on individual ensemble members can be kept low. Of course the many-body system is now described by a collective quantum state, and when the measurement strength is sufficient to resolve the quantum fluctuations associated with a collective observable, backaction will be induced on the collective state and the uncertainty of the measured value can be squeezed [2]. The creation of such quantum correlation has applications in precision measurement and quantum information processing. [3] In this letter we use the linear Faraday effect to probe the spins in an ensemble of laser cooled Cs atoms. [4,5,6] Our setup employs a probe beam tuned near the D 2 transition at 852 nm, whose linear polarization is rotated by an angle proportional to the net spin component along the propagation axis. Measuring the rotation with a shotnoise limited polarimeter provides a weak measurement of the ensemble averaged spin in real time. If the sample is optically thick on resonance, the atom-probe coupling becomes strong enough to allow the collective spin to be measured with resolution below the quantum uncertainty of a many-body spin-coherent state, making it possible to generate quantum correlations within the ensemble. In the limit of large probe detuning, Faraday rotation has been employed as a quantum non-demolition (QND) measurement of the collective spin, and much interest has been focused on its ability to generate spin squeezed states [7,8], to perform sub-shot noise magnetometry [9] and to entangle separated spin ensembles....

We prove a limit theorem for quantum stochastic differential equations with unbounded coefficients which extends the Trotter-Kato theorem for contraction semigroups. From this theorem, general results on the convergence of approximations and singular perturbations are obtained. The results are illustrated in several examples of physical interest.

We consider measurements, described by a positive-operator-valued measure (POVM), whose outcome probabilities determine an arbitrary pure state of a Ddimensional quantum system. We call such a measurement a pure-state informationally complete (PS I-complete) POVM. We show that a measurement with 2D − 1 outcomes cannot be PS I-complete, and then we construct a POVM with 2D outcomes that suffices, thus showing that a minimal PS I-complete POVM has 2D outcomes. We also consider PS I-complete POVMs that have only rank-one POVM elements and construct an example with 3D − 2 outcomes, which is a generalization of the tetrahedral measurement for a qubit. The question of the minimal number of elements in a rank-one PS I-complete POVM is left open.

We present a new procedure for quantum state reconstruction based on weak continuous measurement of an ensemble average. By applying controlled evolution to the initial state, new information is continually mapped onto the measured observable. A Bayesian filter is then used to update the state estimate in accordance with the measurement record. This generalizes the standard paradigm for quantum tomography based on strong, destructive measurements on separate ensembles. This approach to state estimation induces minimal perturbation of the measured system, giving information about observables whose evolution cannot be described classically in real time and opening the door to new types of quantum feedback control.

We demonstrate a fast, robust and non-destructive protocol for quantum state estimation based on continuous weak measurement in the presence of a controlled dynamical evolution. Our experiment uses optically probed atomic spins as a testbed, and successfully reconstructs a range of trial states with fidelities of ∼ 90%. The procedure holds promise as a practical diagnostic tool for the study of complex quantum dynamics, the testing of quantum hardware, and as a starting point for new types of quantum feedback control.PACS numbers: 03.65. Wj, 03.65.Ta, 32.80.Qk Fast, accurate and robust quantum state estimation (tomography) is important for the study of complex quantum systems and dynamics, and promises to be an essential tool in the design and testing of hardware for quantum information processing [1]. Previous demonstrations range from optical [2] to atomic [3] and molecular systems [4], but with few exceptions these procedures have proven too cumbersome to be of use as practical laboratory tools. The procedure of quantum state estimation is usually formulated in terms of strong measurements of an informationally complete set of observables. Each such measurement erases the original quantum state, so the ensemble must be reprepared and the measurement apparatus reconfigured at each step. Here we demonstrate a general approach based instead on continuous weak measurement [5]. Using a weak measurement spreads quantum backaction across the ensemble and dilutes it to the point where it does not significantly affect any individual member. In the absence of backaction the quantum state remains largely intact, subject only to minimal damage from errors in the external drive fields and coupling to the environment. This allows us to estimate the state in a single interrogation of the ensemble, based on the measurement of a fixed observable O and a carefully designed system evolution.In the Heisenberg picture the chosen dynamics leads to a time-dependent observable, O → O(t), and the measurement history can be made informationally complete if the system is controllable, i. e. the dynamics can generate any unitary in SU (d) where d is the dimensionality of Hilbert space. With a non-destructive measurement and near-reversible dynamics, the entire ensemble remains available at the end of the estimation procedure, in a known quantum state that can be restored close to its initial form if desired. In principle, this means that the knowledge gained can be used as a basis for further action, for example real-time feedback control [6] or error correction [1]. From a practical viewpoint our procedure is highly efficient: the ∼ 1ms interrogation time is limited only by the control and measurement bandwidths, and data analysis is performed offline. It is also robust, in the sense that imperfections in the experiment can be included in the analysis if known, or estimated along with the state if they fluctuate in real time.The quantum system used in our laboratory implementation is the total spin-angular momentum (electron plus nu...

We derive a generalized zero-range pseudopotential applicable to all partial wave solutions to the Schrödinger equation based on a delta-shell potential in the limit that the shell radius approaches zero. This properly models all higher order multipole moments not accounted for with a monopolar delta function at the origin, as used in the familiar Fermi pseudopotential for s-wave scattering. By making the strength of the potential energy dependent, we derive self-consistent solutions for the entire energy spectrum of the realistic potential. We apply this to study two particles in an isotropic harmonic trap, interacting through a central potential, and derive analytic expressions for the energy eigenstates and eigenvalues.

We analyze the interplay of chaos, entanglement, and decoherence in a system of qubits whose collective behavior is that of a quantum kicked top. The dynamical entanglement between a single qubit and the rest can be calculated from the mean of the collective spin operators. This allows the possibility of efficiently measuring entanglement dynamics in an experimental setting. We consider a deeply quantum regime and show that signatures of chaos are present in the dynamical entanglement for parameters accessible in an experiment that we propose using cold atoms. The evolution of the entanglement depends on the support of the initial state on regular versus chaotic Floquet eigenstates, whose phase-space distributions are concentrated on the corresponding regular or chaotic eigenstructures. We include the effect of decoherence via a realistic model and show that the signatures of chaos in the entanglement dynamics persist in the presence of decoherence. In addition, the classical chaos affects the decoherence rate itself.

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