This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near-Feshbach resonances in the BCS-BEC crossover.

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Many-Body Physics with Ultracold Gases

Rydberg atoms with principal quantum number $n⪢1$ have exaggerated atomic properties including dipole-dipole interactions that scale as ${n}^{4}$ and radiative lifetimes that scale as ${n}^{3}$. It was proposed a decade ago to take advantage of these properties to implement quantum gates between neutral atom qubits. The availability of a strong long-range interaction that can be coherently turned on and off is an enabling resource for a wide range of quantum information tasks stretching far beyond the original gate proposal. Rydberg enabled capabilities include long-range two-qubit gates, collective encoding of multiqubit registers, implementation of robust light-atom quantum interfaces, and the potential for simulating quantum many-body physics. The advances of the last decade are reviewed, covering both theoretical and experimental aspects of Rydberg-mediated quantum information processing.

Quantum information with Rydberg atoms

The performance of superconducting qubits has improved by several orders of magnitude in the past decade. These circuits benefit from the robustness of superconductivity and the Josephson effect, and at present they have not encountered any hard physical limits. However, building an error-corrected information processor with many such qubits will require solving specific architecture problems that constitute a new field of research. For the first time, physicists will have to master quantum error correction to design and operate complex active systems that are dissipative in nature, yet remain coherent indefinitely. We offer a view on some directions for the field and speculate on its future.

http://science.sciencemag.org/content/sci/339/6124/1169.full.pdf

Superconducting circuits for quantum information: an outlook.

(b) Write out the equations for the time dependence of ρ11, ρ22, ρ12 and ρ21 assuming that a light field interaction V = -μ12Ee iωt + c.c. couples only levels |1> and |2>, and that the excited levels exhibit spontaneous decay. (8 marks) (c) Under steady-state conditions, find the ratio of populations in states |2> and |3>. (3 marks) (d) Find the slowly varying amplitude ̃ ρ 12 of the polarization ρ12 = ̃ ρ 12e iωt . (6 marks) (e) In the limiting case that no decay is possible from intermediate level |3>, what is the ground state population ρ11(∞)? (2 marks) 2. (15 marks total) In a 2-level atom system subjected to a strong field, dressed states are created in the form |D1(n)> = sin θ |1,n> + cos θ |2,n-1> |D2(n)> = cos θ |1,n> sin θ |2,n-1>

The Quantum Theory of Light

Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

http://ieeexplore.ieee.org/iel5/5/31307/01456462.pdf

Linear systems

Feedback loops are central to most classical control procedures A controller compares the signal measured by a sensor (system output) with the target value or set-point It then adjusts an actuator (system input) to stabilize the signal around the target value Generalizing this scheme to stabilize a micro-system's quantum state relies on quantum feedback, which must overcome a fundamental difficulty: the sensor measurements cause a random back-action on the system An optimal compromise uses weak measurements, providing partial information with minimal perturbation The controller should include the effect of this perturbation in the computation of the actuator's operation, which brings the incrementally perturbed state closer to the target Although some aspects of this scenario have been experimentally demonstrated for the control of quantum or classical micro-system variables, continuous feedback loop operations that permanently stabilize quantum systems around a target state have not yet been realized Here we have implemented such a real-time stabilizing quantum feedback scheme following a method inspired by ref 13 It prepares on demand photon number states (Fock states) of a microwave field in a superconducting cavity, and subsequently reverses the effects of decoherence-induced field quantum jumps The sensor is a beam of atoms crossing the cavity, which repeatedly performs weak quantum non-demolition measurements of the photon number The controller is implemented in a real-time computer commanding the actuator, which injects adjusted small classical fields into the cavity between measurements The microwave field is a quantum oscillator usable as a quantum memory or as a quantum bus swapping information between atoms Our experiment demonstrates that active control can generate non-classical states of this oscillator and combat their decoherence, and is a significant step towards the implementation of complex quantum information operations

https://hal-mines-paristech.archives-ouvertes.fr/hal-00637734/document

Real-time quantum feedback prepares and stabilizes photon number states

The state of a microscopic system encodes its complete quantum description, from which the probabilities of all measurement outcomes are inferred. Being a statistical concept, the state cannot be obtained from a single system realization, but can instead be reconstructed from an ensemble of copies through measurements on different realizations. Reconstructing the state of a set of trapped particles shielded from their environment is an important step in the investigation of the quantum-classical boundary. Although trapped-atom state reconstructions have been achieved, it is challenging to perform similar experiments with trapped photons because cavities that can store light for very long times are required. Here we report the complete reconstruction and pictorial representation of a variety of radiation states trapped in a cavity in which several photons survive long enough to be repeatedly measured. Atoms crossing the cavity one by one are used to extract information about the field. We obtain images of coherent states, Fock states with a definite photon number and 'Schrodinger cat' states (superpositions of coherent states with different phases). These states are equivalently represented by their density matrices or Wigner functions. Quasi-classical coherent states have a Gaussian-shaped Wigner function, whereas the Wigner functions of Fock and Schrodinger cat states show oscillations and negativities revealing quantum interferences. Cavity damping induces decoherence that quickly washes out such oscillations. We observe this process and follow the evolution of decoherence by reconstructing snapshots of Schrodinger cat states at successive times. Our reconstruction procedure is a useful tool for further decoherence and quantum feedback studies of fields trapped in one or two cavities.

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Reconstruction of non-classical cavity field states with snapshots of their decoherence

We demonstrate the realization of a quantum register using a string of single neutral atoms which are trapped in an optical dipole trap. The atoms are selectively and coherently manipulated in a magnetic field gradient using microwave radiation. Our addressing scheme operates with a high spatial resolution, and qubit rotations on individual atoms are performed with 99% contrast. In a final readout operation we analyze each individual atomic state. Finally, we have measured the coherence time and identified the predominant dephasing mechanism for our register.

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Neutral atom quantum register

We study in detail the mechanisms causing dephasing of hyperfine coherences of cesium atoms confined by a far-off-resonant standing-wave optical dipole trap [S. Kuhr et al., Phys. Rev. Lett. 91, 213002 (2003)]. Using Ramsey-spectroscopy and spin-echo techniques, we measure the reversible and irreversible dephasing times of the ground-state coherences. We present an analytical model to interpret the experimental data and identify the homogeneous and inhomogeneous dephasing mechanisms. Our scheme to prepare and detect the atomic hyperfine state is applied at the level of a single atom as well as for ensembles of up to 50 atoms.

/pdf/analysis-of-dephasing-mechanisms-in-a-standing-wave-dipole-535dq90f1d.pdf

Analysis of dephasing mechanisms in a standing-wave dipole trap

Repeatedly probing a quantum system restricts its evolution, providing a route for state engineering. Such confinement, described by quantum Zeno dynamics, has now been implemented to generate superposition states in a multi-level Rydberg atom.

/pdf/confined-quantum-zeno-dynamics-of-a-watched-atomic-arrow-jidxxdkbuw.pdf

Igor Dotsenko

Papers

Real-time quantum feedback prepares and stabilizes photon number states

Reconstruction of non-classical cavity field states with snapshots of their decoherence

Neutral atom quantum register

Analysis of dephasing mechanisms in a standing-wave dipole trap

Confined quantum Zeno dynamics of a watched atomic arrow