Rummukainen-Gottlieb's formula on two-particle system with different mass

L\"uscher established a non-perturbative formula to extract the elastic scattering phases from two-particle energy spectrum in a torus using lattice simulations. Rummukainen and Gottlieb further extend it to the moving frame, which is devoted to the system of two identical particles. In this work, we generalize Rummukainen-Gottlieb's formula to the generic two-particle system where two particles are explicitly distinguishable, namely, the masses of the two particles are different. The finite size formula are achieved for both $C_{4v}$ and $C_{2v}$ symmetries. Our analytical results will be very helpful for the study of some resonances, such as kappa, vector kaon, and so on.Comment: matching its published paper and make it concise, and to remove text overlap with arXiv:hep-lat/9503028, arXiv:hep-lat/0404001 by other author

Excited electron-bubble states in superfluid helium-4: a time-dependent density functional approach

We present a systematic study on the excited electron-bubble states in superfluid helium-4 using a time-dependent density functional approach. For the evolution of the 1P bubble state, two different functionals accompanied with two different time-development schemes are used, namely an accurate finite-range functional for helium with an adiabatic approximation for electron versus an efficient zero-range functional for helium with a real-time evolution for electron. We make a detailed comparison between the quantitative results obtained from the two methods, which allows us to employ with confidence the optimal method for suitable problems. Based on this knowledge, we use the finite-range functional to calculate the time-resolved absorption spectrum of the 1P bubble, which in principle can be experimentally determined, and we use the zero-range functional to real-time evolve the 2P bubble for several hundreds of picoseconds, which is theoretically interesting due to the break down of adiabaticity for this state. Our results discard the physical realization of relaxed, metastable 2P electron-bubblesComment: 16 pages, 12 figure

Entanglement-induced electron coherence in a mesoscopic ring with two magnetic impurities

We investigate the Aharonov-Bohm (AB) interference pattern in the electron transmission through a mesoscopic ring in which two identical non-interacting magnetic impurities are embedded. Adopting a quantum waveguide theory, we derive the exact transmission probability amplitudes and study the influence of maximally entangled states of the impurity spins on the electron transmittivity interference pattern. For suitable electron wave vectors, we show that the amplitude of AB oscillations in the absence of impurities is in fact not reduced within a wide range of the electron-impurity coupling constant when the maximally entangled singlet state is prepared. Such state is thus able to inhibit the usual electron decoherence due to scattering by magnetic impurities. We also show how this maximally entangled state of the impurity spins can be generated via electron scattering.Comment: 8 page

Non-Local Quantum Gates: a Cavity-Quantum-Electro-Dynamics implementation

The problems related to the management of large quantum registers could be handled in the context of distributed quantum computation: unitary non-local transformations among spatially separated local processors are realized performing local unitary transformations and exchanging classical communication. In this paper, we propose a scheme for the implementation of universal non-local quantum gates such as a controlled-\gate{NOT} (\cnot) and a controlled-quantum phase gate (\gate{CQPG}). The system we have chosen for their physical implementation is a Cavity-Quantum-Electro-Dynamics (CQED) system formed by two spatially separated microwave cavities and two trapped Rydberg atoms. We describe the procedures to follow for the realization of each step necessary to perform a specific non-local operation.Comment: 12 pages, 5 figures, RevTeX; extensively revised versio

Long-range forces between two excited mercury atoms and associative ionization

The long-range quadrupole-quadrupole ($\sim R^{-5}$) and leading dispersion ($\sim R^{-6}$) interactions between all pairs of excited Hg($6s6p$) $^3P_0$, $^3P_1$, $^3P_2$, and $^1P_1$ atoms are determined. The quadrupole moments are calculated using the {\it ab initio} relativistic configuration-interaction method coupled with many-body perturbation theory. The van der Waals coefficients are approximated using previously calculated static polarizabilities and expressions for the dispersion energy that are validated with similar systems. The long-range interactions are critical for associative ionization in thermal and cold collisions, and are found to be quite different for different pairs of interacting states. Based on this knowledge and the short-range parts of previously calculated potential curves, improved estimates of the chemi-ionization cross sections are obtained.Comment: accepted in Phys Rev

Upper Limit on the Magnetic Dipole Contribution to the 5p-8p Transition in Rb by Use of Ultracold Atom Spectroscopy

We report on hyperfine-resolved spectroscopic measurements of the electric-dipole forbidden 5$p_{3/2} \to 8p_{1/2}$ transition in a sample of ultracold $^{87}$Rb atoms. The hyperfine selection rules enable the weak magnetic-dipole (M1) contribution to the transition strength to be distinguished from the much stronger electric-quadrupole (E2) contribution. An upper limit on the M1 transition strength is determined that is about 50 times smaller than an earlier experimental determination. We also calculate the expected value of the M1 matrix element and find that it is less than the upper limit extracted from the experiment.Comment: 7 pages, 4 figures, 3 table

Optical angular momentum: Multipole transitions and photonics

The premise that multipolar decay should produce photons uniquely imprinted with a measurably corresponding angular momentum is shown in general to be untrue. To assume a one-to-one correlation between the transition multipoles involved in source decay and detector excitation is to impose a generally unsupportable one-to-one correlation between the multipolar form of emission transition and a multipolar character for the detected field. It is specifically proven impossible to determine without ambiguity, by use of any conventional detector, and for any photon emitted through the nondipolar decay of an atomic excited state, a unique multipolar character for the transition associated with its generation. Consistent with the angular quantum uncertainty principle, removal of a detector from the immediate vicinity of the source produces a decreasing angular uncertainty in photon propagation direction, reflected in an increasing range of integer values for the measured angular momentum. In such a context it follows that when the decay of an electronic excited state occurs by an electric quadrupolar transition, for example, any assumption that the radiation so produced is conveyed in the form of “quadrupole photons” is experimentally unverifiable. The results of the general proof based on irreducible tensor analysis invite experimental verification, and they signify certain limitations on quantum optical data transmission

Infrared electron modes in light deformed clusters

Infrared quadrupole modes (IRQM) of the valence electrons in light deformed sodium clusters are studied by means of the time-dependent local-density approximation (TDLDA). IRQM are classified by angular momentum components $\lambda\mu =$20, 21 and 22 whose $\mu$ branches are separated by cluster deformation. In light clusters with a low spectral density, IRQM are unambiguously related to specific electron-hole excitations, thus giving access to the single-electron spectrum near the Fermi surface (HOMO-LUMO region). Most of IRQM are determined by cluster deformation and so can serve as a sensitive probe of the deformation effects in the mean field. The IRQM branch $\lambda\mu =$21 is coupled with the magnetic scissors mode, which gives a chance to detect the latter. We discuss two-photon processes, Raman scattering (RS), stimulated emission pumping (SEP), and stimulated adiabatic Raman passage (STIRAP), as the relevant tools to observe IRQM. A new method to detect the IRQM population in clusters is proposed.Comment: 22 pages, 6 figure

Implications of SU(2) symmetry on the dynamics of population difference in the two-component atomic vapor

We present an exact many body solution for the dynamics of the population difference $N_2-N_1$ induced by an rf-field in the two-component atomic cloud characterized by equal scattering lengths. This situation is very close to the actual JILA experiments with the two-component $^{87}$Rb vapor. We show that no intrinsic decoherence exists for $N_2-N_1$, provided the exact SU(2) symmetry holds. This contrasts with finite dissipation of the normal modes even in the presence of the SU(2) symmetry. The intrinsic decoherence for \$N_2-N_1$ may occur as long as deviations from the exact SU(2) symmetry are taken into account. Such decoherence, however, should be characterized by very long times governed by the smallness of the deviations from the symmetry. We suggest testing the evolution of $N_2-N_1$ by conducting echo-type experiments.Comment: 5 RevTex pages, no figures, typos correcte

On the formation of Wigner molecules in small quantum dots

It was recently argued that in small quantum dots the electrons could crystallize at much higher densities than in the infinite two-dimensional electron gas. We compare predictions that the onset of spin polarization and the formation of Wigner molecules occurs at a density parameter $r_s\approx 4 a_B^*$ to the results of a straight-forward diagonalization of the Hamiltonian matrix