Equilibrium superradiance in a Bose gas

A model of free₄He atoms interacting with radiation exhibits an equilibrium phase transition in which the atomic ground-state Bose condensation is coupled to condensations of virtual photons and virtually excited atoms of the same macroscopic wavelength. The condensed phase has a twofold polarization degeneracy. It is suggested that this might furnish a mechanism for a discrete symmetry-related phase degeneracy of superfluid liquid⁴He required to explain the transition according to Tisza's generalized Gibbsian thermodynamics. A more realistic model would require inclusion of repulsive interactions.Supported in part by the National Science Foundation, Grant DMR76-17467.     

Two-parameter estimation in a matter-wave Sagnac interferometer

We explore the general characteristics of a matter-wave Sagnac interferometer in a two-parameter estimation scheme. We find that the measurement precisions of both parameters cannot reach the Heisenberg limit (HL) simultaneously when the input state is maximally entangled. Only one of the parameters’ uncertainties can approach the HL while the other is scaled by the standard quantum limit. We provide the conditions with which the measurement precision of the specific parameter can reach the HL. We also discuss and figure out the concrete expressions of the constraint conditions for saturating the quantum Cramér–Rao bound. To satisfy these constraint conditions, the evolution time has to be a series of discrete values. Additionally, we calculate the variances of the parameters through some examples under these constraint conditions. The results provided in our work show some intrinsic features of the matter-wave Sagnac interferometer for the two-parameter estimation, which can be valuable in actual experiments.     

Dynamics of matter-wave solitons in a ratchet potential

We study the dynamics of bright solitons formed in a Bose-Einstein condensate with attractive atomic interactions perturbed by a weak bichromatic optical lattice potential. The lattice depth is a biperiodic function of time with a zero mean, which realizes a flashing ratchet for matter-wave solitons. We find that the average velocity of a soliton and the soliton current induced by the ratchet depend on the number of atoms in the soliton. As a consequence, soliton transport can be induced through scattering of different solitons. In the regime when matter-wave solitons are narrow compared to the lattice period the dynamics is well described by the effective Hamiltonian theory.     

Observation of Dicke superradiance at 1.30 μm in atomic Tl vapor

Dicke superradiance in the 1.30-μm $\text{7}{}^2\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{→ 7}{}^2\text{S}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ transition in Tl vapor has been induced by a 379.1-nm pulsed dye laser. Superradiant delays of up to 12 nsec have been observed.     

Fluctuation in superradiance

The fluctuation of the intensity of superradiant pulse is calculated by applying a general asymptotic evaluation method of quantal macrovariables to a superradiant master equation. It is shown that the fluctuation of superradiant intensity is proportional to the cube of the number of the relevant atoms. The time-dependence of the proportional coefficient has been evaluated explicitly. It is predicted that there occurs an enhancement of fluctuation of superradiant intensity at an intermediate time. The intensity and fluctuation of higher order are also calculated. General expressions of expansion coefficients of a generating function are also given rigorously.     

Phase transition in a generalized Dicke model of superradiance

By means of the use of the “gap equations”, we calculate the thermodynamic properties of a sufficiently general Dicke model. We obtain the general relations which correspond to the condition of second-order phase transition from the normal to the superradiant state.     

Time reversal in matter-wave optics

The evolution of atomic wave packets experiencing so-called comoving potential pulses is examined theoretically, in the framework of the stationary-phase approximation. The negative refraction induced by this potential is a characteristic property of negative-index media, the atomic counterpart of negative-index materials of light optics. A novel process, specific of negative-index for matter waves, is evidenced, namely a narrowing of the wave packet transiently counterbalancing the natural spreading. This is the manifestation of a general property of negative-index media, i.e. a time reversal effect. It is shown that, for a statistical ensemble of wave packets leading to a moderate dispersion of the times of flight, this time reversal phenomenon should be observable.     

Induced superradiance in activated crystals

The observation of superradiance in activated crystals induced by propagation of a short coherent pulse through an inverted sample is proposed. The theoretical estimation of the induced superradiance in Nd: YAG is given.     

Phase transition to superradiance in a multicomponent system

Abtract The study deals with the ground-state energy transition of a multicomponent atomic system from its normal state to the superradiant state when interacting with a multimode quantized electromagnetic field. The threshold conditions are determined.Alexander-von-Humboldt awardee     

Optical superradiance in solids

The characteristic features of theoretically describing and experimentally observing superradiance in a diphenyl crystal containing pyrene are discussed together with the possibility of using optical superradiance in crystals as a method for investigating relaxation processes which involve the participation of lattice and pseudolocalized phonons. The possibilities of this method are compared with those of other coherent spectroscopic methods.Scientific-Research Institute of Special Secondary Education, Kazan. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 86–93, July, 1993.     

Quantum reflection of bright matter-wave solitons

We propose the use of bright matter-wave solitons formed from Bose-Einstein condensates with attractive interactions to probe and study quantum reflection from a solid surface at normal incidence. We demonstrate that the presence of attractive interatomic interactions leads to a number of advantages for the study of quantum reflection. The absence of dispersion as the soliton propagates allows precise control of the velocity normal to the surface and for much lower velocities to be achieved. Numerical modelling shows that the robust, self-trapped nature of bright solitons leads to a clean reflection from the surface, limiting the disruption of the density profile and permitting accurate measurements of the reflection probability.     

Classical statistical mechanics of a lattice model of superradiance

A classical model of the interaction of N two-level atoms with the radiation field discretized on a lattice, having particular relevance for superradiance, is discussed. By evaluating the corresponding partition function the threshold condition for the occurrence of a second-order phase transition is derived. A comparison with previous work, where a finite number of field modes was considered, is also given.     

Coupled matter-wave solitons in optical lattices

We make use of a potential model to study the dynamics of two coupled matter-wave or Bose-Einstein condensate (BEC) solitons loaded in optical lattices. With separate attention to linear and nonlinear lattices we find some remarkable differences for response of the system to effects of these lattices. As opposed to the case of linear optical lattice (LOL), the nonlinear lattice (NOL) can be used to control the mutual interaction between the two solitons. For a given lattice wave number k, the effective potentials in which the two solitons move are such that the well (V_eff(NOL)), resulting from the juxtaposition of soliton interaction and nonlinear lattice potential, is deeper than the corresponding well V_eff(LOL). But these effective potentials have opposite k dependence in the sense that the depth of V_eff(LOL) increases as k increases and that of V_eff(NOL) decreases for higher k values. We verify that the effectiveness of optical lattices to regulate the motion of the coupled solitons depends sensitively on the initial locations of the motionless solitons as well as values of the lattice wave number. For both LOL and NOL the two solitons meet each other due to mutual interaction if their initial locations are taken within the potential wells with the difference that the solitons in the NOL approach each other rather rapidly and take roughly half the time to meet as compared with the time needed for such coalescence in the LOL. In the NOL, the soliton profiles can move freely and respond to the lattice periodicity when the separation between their initial locations are as twice as that needed for a similar free movement in the LOL. We observe that, in both cases, slow tuning of the optical lattices by varying k with respect to a time parameter τ drags the oscillatory solitons apart to take them to different locations. In our potential model the oscillatory solitons appear to propagate undistorted. But a fully numerical calculation indicates that during evolution they exhibit decay and revival.     

Generation of nonclassical states in a large detuning cavity

By using the theory of cavity QED, we study the system in which a two-level atom interacts with a cavity in the case of large detuning. Through the selective detecting of atomic state, Schrodinger cat states and entangled coherent states are easily generated. When the atom is driven by a weak classical field and the cavity field is in the Schrodinger cat state, we study the conditions of generating the Fock states and the maximal success probability. The maximal success probability in our scheme is larger than the previous one.     

Temperature dependence of superradiance intensity

Using the idea of exchange interaction in a system of two-level atoms participating in a superradiance process, we derive from first principles the superradiance Hamiltonian of such a system, which is found to be analogous to the Heisenberg Hamiltonian. We consistently calculate the coupling constant of the interaction that leads to the emergence of a superradiance state in the system. We also predict the existence of isospin excitations in the superradiance state, whose presence reduces the intensity of the corresponding superradiance pulse. Finally, we calculate the temperature dependence of the intensity of the superradiance pulse and find it be analogous to the Bloch T ^3/2-law for spin systems. Zh. éksp. Teor. Fiz. 116, 1148–1160 (October 1999)     

High-order-harmonic generation and superradiance in a seeded free-electron laser

Higher order harmonic generation in a free-electron laser amplifier operating in the superradiant regime [R. H. Dicke, Phys. Rev. 93, 99 (1954).] has been observed. Superradiance has been induced by seeding a single-pass amplifier with the second harmonic of a Ti:sapphire laser, generated in a β-Barium borate crystal, at seed intensities comparable to the free-electron laser saturation intensity. Pulse energy and spectral distributions of the harmonics up to the 11th order have been measured and compared with simulations.     

Quantum entanglement via superradiance of a Bose-Einstein condensate

We adopt the coherence and built-in swap mechanism in sequential superradiance as a tool for obtaining continuous-variable (electric/magnetic fields) quantum entanglement of two counter-propagating pulses emitted from the two end-fire modes. In the first-sequence, end-fire modes are entangled with the side modes. In the second sequence, this entanglement is swapped to in between the two opposite end-fire modes. Additionally, we also examine the photon number correlations. No quantum correlations is observed in this variable.     

Generalized Fokker-Planck equation in superradiance theory

An alternative projector technique approach to the Bonifacio-Schwendimann-Haake model of superradiance is presented. A bilinear master equation for the probability distributions of photon number and atomic excitation is derived. In the case of very large numbers of atoms we end up with a generalized Fokker-Planck equation for atoms.     

Photon echo under two-quantum excitation of superradiance in a cavity

The superradiance, photon echo, and coherence transformation in three-level cascade-type atoms have been theoretically investigated for the case where the frequency of an optically allowed transition from the upper level coincides with the cavity frequency.