Chemical potential for light by parametric coupling

Usually photons are not conserved in their interaction with matter. Consequently, for the thermodynamics of photons, while we have a concept of temperature for energy conservation, there is no equivalent chemical potential for particle number conservation. However, the notion of a chemical potential is crucial in understanding a wide variety of single- and many-body effects, from transport in conductors and semiconductors to phase transitions in electronic and atomic systems. Here we show how a direct modification of the system-bath coupling via parametric oscillation creates an effective chemical potential for photons even in the thermodynamic limit. In particular, we show that the photonic system equilibrates to the temperature of the bath, with a tunable chemical potential that is set by the frequency of the parametric coupler. Specific implementations, using circuit-QED or optomechanics, are feasible using current technologies, and we show a detailed example demonstrating the emergence of Mott insulator-superfluid transition in a lattice of nonlinear oscillators. Our approach paves the way for quantum simulation, quantum sources, and even electron-like circuits with light.Comment: 9 pages, 5 figures, v3: extended discussions, similar to published version at PR

Universal scaling in BCS superconductivity in two dimensions in non-s waves

The solutions of a renormalized BCS model are studied in two space dimensions in $s$, $p$ and $d$ waves for finite-range separable potentials. The gap parameter, the critical temperature $T_c$, the coherence length $\xi$ and the jump in specific heat at $T_c$ as a function of zero-temperature condensation energy exhibit universal scalings. In the weak-coupling limit, the present model yields a small $\xi$ and large $T_c$ appropriate to those for high-$T_c$ cuprates. The specific heat, penetration depth and thermal conductivity as a function of temperature show universal scaling in $p$ and $d$ waves.Comment: 11 pages, LATEX, 4 postscript figures embedded using eps

Self-trapping of a binary Bose-Einstein condensate induced by interspecies interaction

The problem of self-trapping of a Bose-Einstein condensate (BEC) and a binary BEC in an optical lattice (OL) and double well (DW) is studied using the mean-field Gross-Pitaevskii equation. For both DW and OL, permanent self-trapping occurs in a window of the repulsive nonlinearity $g$ of the GP equation: $g_{c1}<g<g_{c2}$. In case of OL, the critical nonlinearities $g_{c1}$ and $g_{c2}$ correspond to a window of chemical potentials $\mu_{c1}<\mu<\mu_{c2}$ defining the band gap(s) of the periodic OL. The permanent self-trapped BEC in an OL usually represents a breathing oscillation of a stable stationary gap soliton. The permanent self-trapped BEC in a DW, on the other hand, is a dynamically stabilized state without any stationary counterpart. For a binary BEC with intraspecies nonlinearities outside this window of nonlinearity, a permanent self trapping can be induced by tuning the interspecies interaction such that the effective nonlinearities of the components fall in the above window

Long-range interactions of hydrogen atoms in excited states. III. nS-1S interactions for n >= 3

The long-range interaction of excited neutral atoms has a number of interesting and surprising properties, such as the prevalence of long-range, oscillatory tails, and the emergence of numerically large can der Waals C_6 coefficients. Furthermore, the energetically quasi-degenerate nP states require special attention and lead to mathematical subtleties. Here, we analyze the interaction of excited hydrogen atoms in nS states (3 <= n <= 12) with ground-state hydrogen atoms, and find that the C_6 coefficients roughly grow with the fourth power of the principal quantum number, and can reach values in excess of 240,000 (in atomic units) for states with n = 12. The nonretarded van der Waals result is relevant to the distance range R << a_0/alpha, where a_0 is the Bohr radius and alpha is the fine-structure constant. The Casimir-Polder range encompasses the interatomic distance range a_0/alpha << R << hbar c/L, where L is the Lamb shift energy. In this range, the contribution of quasi-degenerate excited nP states remains nonretarded and competes with the 1/R^2 and 1/R^4 tails of the pole terms which are generated by lower-lying mP states with 2 <= m <= n-1, due to virtual resonant emission. The dominant pole terms are also analyzed in the Lamb shift range R >> hbar c/L. The familiar 1/R^7 asymptotics from the usual Casimir-Polder theory is found to be completely irrelevant for the analysis of excited-state interactions. The calculations are carried out to high precision using computer algebra in order to handle a large number of terms in intermediate steps of the calculation, for highly excited states.Comment: 17 pages; RevTe

Linear to quadratic crossover of Cooper pair dispersion relation

Cooper pairing is studied in three dimensions to determine its binding energy for all coupling using a general separable interfermion interaction. Also considered are Cooper pairs (CPs) with nonzero center-of-mass momentum (CMM). A coupling-independent {\it linear} term in the CMM dominates the pair excitation energy in weak coupling and/or high fermion density, while the more familiar quadratic term prevails only in the extreme low-density (i.e., vacuum) limit for any nonzero coupling. The linear-to-quadratic crossover of the CP dispersion relation is analyzed numerically, and is expected to play a central role in a model of superconductivity (and superfluidity) simultaneously accommodating a BCS condensate as well as a Bose-Einstein condensate of CP bosons.Comment: 13 pages plus 2 figure

X-ray observations of the hot phase in Sgr~A*

We analyze 134 ks Chandra ACIS-I observations of the Galactic Centre (GC) performed in July 2011. The X-ray image with the field of view $17' \times 17'$ contains the hot plasma surrounding the Sgr~A*. The obtained surface brightness map allow us to fit Bondi hot accretion flow to the innermost hot plasma around the GC. We have fitted spectra from region up to $5"$ from Sgr~A* using a thermal bremsstrahlung model and four Gaussian profiles responsible for K$_{\alpha}$ emission lines of Fe, S, Ar, and Ca. The X-ray surface brightness profile up to $3"$ from Sgr~A* found in our data image, was successfully fitted with the dynamical model of Bondi spherical accretion. By modelling the surface brightness profile, we derived the temperature and number density profiles in the vicinity of the black hole. The best fitted model of spherical Bondi accretion shows that this type of flow works only up to $3"$ and implies outer plasma density and temperature to be: $n_{\rm e}^{\rm out}=18.3 \pm {0.1}$ cm$^{-3}$ and $T_{\rm e}^{\rm out}= 3.5 \pm {0.3}$ keV respectively. We show that the Bondi flow can reproduce observed surface brightness profile up to $3"$ from Sgr~A* in the Galactic Center. This result strongly suggests the position of stagnation radius in the complicated dynamics around GC. The Faraday rotation computed from our model towards the pulsar PSR J1745-2900 near the GC agrees with the observed one, recently reported.Comment: 10 pages, 7 figures, accepted for publication in A&

Entanglement witness operator for quantum teleportation

The ability of entangled states to act as resource for teleportation is linked to a property of the fully entangled fraction. We show that the set of states with their fully entangled fraction bounded by a threshold value required for performing teleportation is both convex and compact. This feature enables for the existence of hermitian witness operators the measurement of which could distinguish unknown states useful for performing teleportation. We present an example of such a witness operator illustrating it for different classes of states.Comment: Minor revisions to match the published version. Accepted for publication in Physical Review Letter

Dynamics of quasi-one-dimensional bright and vortex solitons of a dipolar Bose-Einstein condensate with repulsive atomic interaction

By numerical and variational analysis of the three-dimensional Gross-Pitaevskii equation we study the formation and dynamics of bright and vortex-bright solitons in a cigar-shaped dipolar Bose-Einstein condensate for large repulsive atomic interactions. Phase diagram showing the region of stability of the solitons is obtained. We also study the dynamics of breathing oscillation of the solitons as well as the collision dynamics of two solitons at large velocities. Two solitons placed side-by-side at rest coalesce to form a stable bound soliton molecule due to dipolar attraction.Comment: To obtain the included video clips S1, S2, S3 and S4, please download sourc