Applying matrix product operators to model systems with long-range interactions

An algorithm is presented which computes a translationally invariant matrix product state approximation of the ground state of an infinite 1D system; it does this by embedding sites into an approximation of the infinite ``environment'' of the chain, allowing the sites to relax, and then merging them with the environment in order to refine the approximation. By making use of matrix product operators, our approach is able to directly model any long-range interaction that can be systematically approximated by a series of decaying exponentials. We apply our techniques to compute the ground state of the Haldane-Shastry model and present results.Comment: 7 pages, 3 figures; manuscript has been expanded and restructured in order to improve presentation of the algorith

Magnetic Trapping of Cold Bromine Atoms

Magnetic trapping of bromine atoms at temperatures in the milliKelvin regime is demonstrated for the first time. The atoms are produced by photodissociation of Br$_2$ molecules in a molecular beam. The lab-frame velocity of Br atoms is controlled by the wavelength and polarization of the photodissociation laser. Careful selection of the wavelength results in one of the pair of atoms having sufficient velocity to exactly cancel that of the parent molecule, and it remains stationary in the lab frame. A trap is formed at the null point between two opposing neodymium permanent magnets. Dissociation of molecules at the field minimum results in the slowest fraction of photofragments remaining trapped. After the ballistic escape of the fastest atoms, the trapped slow atoms are only lost by elastic collisions with the chamber background gas. The measured loss rate is consistent with estimates of the total cross section for only those collisions transferring sufficient kinetic energy to overcome the trapping potential

Mechanical Entanglement via Detuned Parametric Amplification

We propose two schemes to generate entanglement between a pair of mechanical oscillators using parametric amplification. In contrast to existing parametric drive-based protocols, both schemes operate in the steady-state. Using a detuned parametric drive to maintain equilibrium and to couple orthogonal quadratures, our approach can be viewed as a two-mode extension of previous proposals for parametric squeezing. We find that robust steady-state entanglement is possible for matched oscillators with well-controlled coupling. In addition, one of the proposed schemes is robust to differences in the damping rates of the two oscillators.Comment: 13 pages, 2 figure

Detuned Mechanical Parametric Amplification as a Quantum Non-Demolition Measurement

Recently it has been demonstrated that the combination of weak-continuous position detection with detuned parametric driving can lead to significant steady-state mechanical squeezing, far beyond the 3 dB limit normally associated with parametric driving. In this work, we show the close connection between this detuned scheme and quantum non-demolition (QND) measurement of a single mechanical quadrature. In particular, we show that applying an experimentally realistic detuned parametric drive to a cavity optomechanical system allows one to effectively realize a QND measurement despite being in the bad-cavity limit. In the limit of strong squeezing, we show that this scheme offers significant advantages over standard backaction evasion, not only by allowing operation in the weak measurement and low efficiency regimes, but also in terms of the purity of the mechanical state.Comment: 17 pages, 2 figure

Semiclassical theory of cavity-assisted atom cooling

We present a systematic semiclassical model for the simulation of the dynamics of a single two-level atom strongly coupled to a driven high-finesse optical cavity. From the Fokker-Planck equation of the combined atom-field Wigner function we derive stochastic differential equations for the atomic motion and the cavity field. The corresponding noise sources exhibit strong correlations between the atomic momentum fluctuations and the noise in the phase quadrature of the cavity field. The model provides an effective tool to investigate localisation effects as well as cooling and trapping times. In addition, we can continuously study the transition from a few photon quantum field to the classical limit of a large coherent field amplitude.Comment: 10 pages, 8 figure

Explosion of white dwarfs harboring hybrid CONe cores

Recently, it has been found that off-centre carbon burning in a subset of intermediate-mass stars does not propagate all the way to the center, resulting in a class of hybrid CONe cores. Here, we consider the possibility that stars hosting these hybrid CONe cores might belong to a close binary system and, eventually, become white dwarfs accreting from a non-degenerate companion at rates leading to a supernova explosion. We have computed the hydrodynamical phase of the explosion of Chandrasekhar-mass white dwarfs harboring hybrid cores, assuming that the explosion starts at the center, either as a detonation (as may be expected in some degenerate merging scenarios) or as a deflagration (that afterwards transitions into a delayed detonation). We assume these hybrid cores are made of a central CO volume, of mass M(CO), surrounded by an ONe shell. We show that, in case of a pure detonation, a medium-sized CO-rich region, M(CO)<0.4 Msun, results in the ejection of a small fraction of the mantle while leaving a massive bound remnant. Part of this remnant is made of the products of the detonation, Fe-group nuclei, but they are buried in its inner regions, unless convection is activated during the ensuing cooling and shrinking phase of the remnant. In contrast, and somehow paradoxically, delayed detonations do not leave remnants but for the minimum M(CO) we have explored, M(CO)=0.2 Msun, and even in this case the remnant is as small as 0.13 Msun. The ejecta produced by these delayed detonations are characterized by slightly smaller masses of 56Ni and substantially smaller kinetic energies than obtained for a delayed detonation of a 'normal' CO white dwarf. The optical emission expected from these explosions would hardly match the observational properties of typical Type Ia supernovae, although they make interesting candidates for the subluminous class of SN2002cx-like or SNIax.Comment: Accepted for Astronomy and Astrophysics, 11 pages, 4 figure

On the suppression of the diffusion and the quantum nature of a cavity mode. Optical bistability; forces and friction in driven cavities

A new analytical method is presented here, offering a physical view of driven cavities where the external field cannot be neglected. We introduce a new dimensionless complex parameter, intrinsically linked to the cooperativity parameter of optical bistability, and analogous to the scaled Rabbi frequency for driven systems where the field is classical. Classes of steady states are iteratively constructed and expressions for the diffusion and friction coefficients at lowest order also derived. They have in most cases the same mathematical form as their free-space analog. The method offers a semiclassical explanation for two recent experiments of one atom trapping in a high Q cavity where the excited state is significantly saturated. Our results refute both claims of atom trapping by a quantized cavity mode, single or not. Finally, it is argued that the parameter newly constructed, as well as the groundwork of this method, are at least companions of the cooperativity parameter and its mother theory. In particular, we lay the stress on the apparently more fundamental role of our structure parameter.Comment: 24 pages, 7 figures. Submitted to J. Phys. B: At. Mol. Opt. Phy

Adaptive homodyne measurement of optical phase

We present an experimental demonstration of the power of real-time feedback in quantum metrology, confirming a theoretical prediction by Wiseman regarding the superior performance of an adaptive homodyne technique for single-shot measurement of optical phase. For phase measurements performed on weak coherent states with no prior knowledge of the signal phase, we show that the variance of adaptive homodyne estimation approaches closer to the fundamental quantum uncertainty limit than any previously demonstrated technique. Our results underscore the importance of real-time feedback for reaching quantum performance limits in coherent telecommunication, precision measurement and information processing.Comment: RevTex4, color PDF figures (separate files), submitted to PR