Ground State Occupation Research Articles

Spontaneous phase condensation of CdTe exciton‐polaritons

AbstractWe have studied CdTe/CdMgTe microcavity samples containing 4 quantum wells and characterized by a vacuum field Rabi‐splitting of 13.2 meV. Electron‐hole pairs were excited at 7.3K by linearly‐polarized light at 1.74 eV provided by a Ti:sapphire laser operating in the pulsed mode (at 80 MHz rate). Spectroscopic imaging in reciprocal space as well as near‐field spectroscopy show that, above a critical stimulation threshold, polaritons in our microcavity undergo a spontaneous transition to a condensed phase characterized by the massive occupation of the polariton ground state. The coherence of this quantum state is evidenced by the spectral and angular narrowing of its emission. We point out the conditions which should be fulfilled to achieve BEC of microcavity polaritons. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Interband and intraband photocurrent of self-assembled InAs/InAlAs/InP nanostructures

The interband and intraband photocurrent properties of InAs/InAlAs/InP nanostructureshave been studied. The doping effect on the photoluminescence properties of the quantumdots and the anisotropy of the quantum wire interband photocurrent properties arepresented and discussed. With the help of interband excitation, an intraband photocurrentsignal of the InAs nanostructures is observed. With the increase of the interband excitationpower, the intraband photocurrent signal first increases and then decreases, which can beexplained by the variance of the ground state occupation of the InAs nanostructures andthe change of the mobility and lifetime of the electrons. The temperature dependence of theintraband photocurrent signal of the InAs nanostructures is also investigated.

Quantum phase transition in the [formula omitted] boson system

The quantum phase transitional behavior of the U ( 3 ) boson model is studied. Low-lying levels, overlaps of wavefunctions with those in the d-wave dominant and s- and d-wave mixed phases, as well as ground state occupation probabilities of s- and d-components are examined as functions of the control parameter and the number of particles. The results indicated that the s- and d-wave component change in the wavefunction possibly is a first order quantum phase transition in the large N limit.

Bath-Assisted Cooling of Spins

A suitable sequence of sharp pulses applied to a spin coupled to a bosonic bath can cool its state, i.e., increase its polarization or ground state occupation probability. Starting from an unpolarized state of the spin in equilibrium with the bath, one can reach very low temperatures or sizable polarizations within a time shorter than the decoherence time. Both the bath and external fields are necessary for the effect, which comes from the backreaction of the spin on the bath. This method can be applied to cool at once a disordered ensemble of spins.

Finite one-dimensional impenetrable Bose systems: Occupation numbers

Bosons in the form of ultra cold alkali atoms can be confined to a one dimensional (1d) domain by the use of harmonic traps. This motivates the study of the ground state occupations $\lambda_i$ of effective single particle states $\phi_i$, in the theoretical 1d impenetrable Bose gas. Both the system on a circle and the harmonically trapped system are considered. The $\lambda_i$ and $\phi_i$ are the eigenvalues and eigenfunctions respectively of the one body density matrix. We present a detailed numerical and analytic study of this problem. Our main results are the explicit scaled forms of the density matrices, from which it is deduced that for fixed $i$ the occupations $\lambda_i$ are asymptotically proportional to $\sqrt{N}$ in both the circular and harmonically trapped cases.

Ground-state properties of hard-core bosons in one-dimensional harmonic traps

The one-particle density matrices for hard core bosons in a one-dimensional harmonic trap are computed numerically for systems with up to 160 bosons. Diagonalization of the density matrix shows that the many-body ground state is not Bose-Einstein condensed. The ground state occupation, the amplitude of the lowest natural orbital, and the zero momentum peak height scale as powers of the particle number, and the corresponding exponents are related to each other. Close to its diagonal, the density matrix for hard core bosons is similar to the one of noninteracting fermions.

Counting statistics and fluctuations in Bose–Einstein condensation

For a system of N Bose atoms, we propose a natural probability distribution for the occupation numbers. The counting statistics only depends on the probabilities of occupation of the single-particle states. Fluctuations of the occupation numbers are related in a simple way with the corresponding probabilities. The case of N ideal bosons trapped in a symmetric three-dimensional harmonic potential is analyzed. In this case, fluctuations of the condensate display a physically expected behavior. When the thermodynamic limit is considered, we obtain analytic expressions for the counting statistics and fluctuations of the ground estate occupation number. The temperature of maximum fluctuations of the ground state occupation number is proposed in order to characterize in an unambiguous way the apparition of a macroscopic condensate fraction.

Painlevé Transcendent Evaluations of Finite System Density Matrices for 1d Impenetrable Bosons

The recent experimental realisation of a one-dimensional Bose gas of ultra cold alkali atoms has renewed attention on the theoretical properties of the impenetrable Bose gas. Of primary concern is the ground state occupation of effective single particle states in the finite system, and thus the tendency for Bose-Einstein condensation. This requires the computation of the density matrix. For the impenetrable Bose gas on a circle we evaluate the density matrix in terms of a particular Painlev\'e VI transcendent in $\sigma$-form, and furthermore show that the density matrix satisfies a recurrence relation in the number of particles. For the impenetrable Bose gas in a harmonic trap, and with Dirichlet or Neumann boundary conditions, we give a determinant form for the density matrix, a form as an average over the eigenvalues of an ensemble of random matrices, and in special cases an evaluation in terms of a transcendent related to Painlev\'e V and VI. We discuss how our results can be used to compute the ground state occupations.

Intraband and interband photocurrent spectroscopy and induced dipole moments of InAs/GaAs(001) quantum dots in n–i–n photodetector structures

We have investigated normal-incidence intra- and interband spectra of self-assembled steep InAs/GaAs(001) quantum dots (QDs) with an average height of ∼8.0 nm and average base width of ∼21 nm placed in n–i(QDs)–n photodetector structures. The ground state occupation of the QDs in the n–i(QDs)–n configuration is examined and used to assign observed intraband transitions. A photovoltaic effect in intraband photocurrent is observed and shown to arise from induced dipole moments. Stark shift in interband photocurrent spectroscopy reveals the presence and direction of interband transition induced dipoles, making this study the first to determine both intra- and interband dipoles in the same ensemble of QDs.

Canonical statistics of trapped ideal and interacting Bose gases

The mean ground-state occupation number and condensate fluctuations of interacting and noninteracting Bose gases confined in a harmonic trap are considered by using a canonical ensemble approach. To obtain the mean ground-state occupation number and the condensate fluctuations, an analytical description for the probability distribution function of the condensate is provided directly starting from the analysis of the partition function of the system. For the ideal Bose gas, the probability distribution function is found to be a Gaussian one for the case of the harmonic trap. For the interacting Bose gas, using a unified approach the condensate fluctuations are calculated based on the lowest-order perturbation method and on Bogoliubov theory. It is found that the condensate fluctuations based on the lowest-order perturbation theory follow the law $〈{\ensuremath{\delta}}^{2}{N}_{0}〉\ensuremath{\sim}N,$ while the fluctuations based on Bogoliubov theory behave as ${N}^{4/3}.$

Interacting one-dimensional Bose gas: Beyond Bogolyubov

The properties of a one-dimensional system of bosons interacting via a repulsive delta-function potential are studied here using a modified Bogolyubov method. The motivation for the modification is twofold: First, to cure an internal inconsistency that predicts a single-particle ground-state occupancy of minus infinity when the Bogolyubov scheme is applied to this model. Second, to abandon the initial assumption---at odds with the exact result---of a macroscopically occupied single-particle ground-state. Whereas the Bogolyubov scheme uses the lowest-energy-single-particle state as a reservoir for the other states, our method uses, for each single-particle state, all single-particle states of lower energy collectively as a reservoir. This not only removes the inconsistency but also allows us to estimate the ground-state energy in much better agreement with the exact result.

Bose-Einstein Condensation in an Axially Symmetric Mesoscopic System

The role played by the effective dimensionality in the thermodynamic behaviour as well as in the ground-state population of an ideal mesoscopic system of non-interacting bosons, is numerically studied. Although Bose-Einstein condensation has not been predicted for one-dimensional systems, the heat capacity and ground state occupation behaviours give signatures of the possible condensation like in three- and two-dimensional limits, for a symmetrical confinement potential. It is found that the maximum values of both, critical and transition temperatures, increase as the system becomes two-dimensional, which could facilitate the experimental efforts.

Reconstructing the time evolution of a quantized oscillator

A method is proposed that allows one to reconstruct the unitary time-evolution matrix of a quantized oscillator. It combines coherent splitting and displacement of the quantum state after the interaction of interest with a subsequent measurement of the occupation of the oscillator ground state. The time-evolution matrix in number basis is then obtained by a twofold Fourier transform of the measured data. It is shown how to realize such a method for the case of the quantized center-of-mass motion of a trapped atom. Simulations for particular examples of interactions demonstrate the feasibility of the reconstruction method even in the presence of noisy data.

Condensate statistics in interacting and ideal dilute bose gases

We obtain analytical formulas for the statistics, in particular, for the characteristic function and all cumulants, of the Bose-Einstein condensate in dilute weakly interacting and ideal equilibrium gases in the canonical ensemble via the particle-number-conserving operator formalism of Girardeau and Arnowitt. We prove that the ground-state occupation statistics is not Gaussian even in the thermodynamic limit. We calculate the effect of Bogoliubov coupling on suppression of ground-state occupation fluctuations and show that they are governed by a pair-correlation, squeezing mechanism.

Evidence of configuration interaction in resonant X-ray scattering from rare earths at the M 4,5-thresholds with final 4p excitation

We present the first data on the systematics of the resonant M 4,5-scattering (3d 94f n+1 excitation; n ground state occupation) from rare earths with a final state 4p hole. We give evidence for the final state interaction of the 4f n+1 4p 5 configuration with the configurations (4d 84f n+2 ) and ( 4 d 84 f n+1ε; ε means continuum). The interaction is stronger at the M 4 threshold. Data on La, Ce 7Rh 3, CeRh 2 and Gd are given.

Nonergodic behavior of interacting bosons in harmonic traps

We study the time evolution of a system of interacting bosons in a harmonic trap. In the low-energy regime, the quantum system is not ergodic and displays rather large fluctuations of the ground-state occupation number. In the high-energy regime of classical physics we find nonergodic behavior for modest numbers of trapped particles. We give two conditions that assure the ergodic behavior of the quantum system even below the condensation temperature.

Statistical mechanics of ideal Bose atoms in a harmonic trap

For ideal Bose atoms in an isotropic harmonic trap, we consider thermodynamic variables obtained from microcanonical, canonical, and grand canonical ensembles, each with certain variables specified and other variables fluctuating. For the first two of these ensembles, we derive recursion relations that link partition functions for different dimensions. We discuss fluctuations in general, and obtain expressions for variances of the atom number N, the chemical potential \ensuremath{\mu}, and the temperature T for small, Gaussian fluctuations in the grand canonical ensemble. Then from our recursion relations and others given elsewhere, we obtain probability distributions for N, for ground-state occupation number ${n}_{0}$, for \ensuremath{\mu}, and for T. Below the critical temperature, the shape of the distributions for N, ${n}_{0},$ and \ensuremath{\mu} are definitely not Gaussian for the grand canonical ensemble. For given temperature and small N, we find that the chemical potential values pertaining to the three ensembles differ. We compare the specific-heat function ${C}_{N}(T)$ for the three ensembles and propose to use the minimum of ${\mathrm{dC}}_{N}/dT$ to define the critical temperature to facilitate comparisons with similar configurations of interacting atoms.

Strong hybridization in vanadium oxides: evidence from photoemission and absorption spectroscopy

We present x-ray photoemission spectra of the vanadium oxides , and , and their analysis in terms of a simple cluster model based on the Anderson impurity Hamiltonian. The electronic structure of these materials is characterized by a strong V 3d-O 2p hybridization energy which exceeds the energy scales related to on-site Coulomb correlation and metal-ligand charge transfer. This result is at variance with the usual Mott-Hubbard picture, but agrees with recent studies of other early 3d transition metal compounds. The V 3d ground-state occupations obtained by the cluster-model analysis are considerably higher than the values derived from the formal valencies. Covalency also affects the exchange splitting observed in the V 3s core-hole spectra. X-ray absorption measurements and resonant photoemission spectroscopy at the V 2p-3d threshold provide further evidence for a strong V 3d-O 2p coupling.

Coulomb Charging Effect in Self-Assembled Ge Quantum Dots Studied by Admittance Spectroscopy

Quantum confined energy levels and the Coulomb charging effect of holes in self-assembled Ge dots embedded in Si barriers are studied using admittance spectroscopy at temperatures above 100 K. Ground state and first excited state occupancies of five to seven holes are identified by varying the Fermi-level position under different applied bias voltages in the admittance measurements. Hole-capture cross sections of the quantum levels are found to be extremely large and energy dependent.

Iron(III) and iron(II) complexes of 1-thia-4,7-diazacyclononane ([9]aneN2S) and 1,4-dithia-7-azacyclononane ([9]aneNS2). X-Ray structural analyses, magnetic susceptibility, Mössbauer, EPR and electronic spectroscopy †

The complexes [Fe([9]aneN2S)2][ClO4]2, [Fe([9]aneN2S)2][ClO4]3 and [Fe([9]aneNS2)2][ClO4]2 ([9]aneN2S = 1-thia-4,7-diazacyclononane and [9]aneNS2 = 1,4-dithia-7-azacyclononane) have been prepared and the latter two characterised by X-ray crystallography. The Mossbauer spectra (isomer shift/mm s–1, quadrupole splitting/mm s–1, 4.2 K) for [Fe([9]aneN2S)2][ClO4]2 (0.52, 0.57), [Fe([9]aneN2S)2][ClO4]3 (0.25, 2.72) and [Fe([9]aneNS2)2][ClO4]2 (0.43, 0.28) are typical for iron(II) and iron(III) complexes. Variable-temperature susceptibility measurements for [Fe([9]aneN2S)2][ClO4]2 (2–300 K) revealed temperature-dependent behaviour in both the solid state [2.95 µB (300 K)–0.5 µB (4.2 K)] and solution (ΔH 0 20–22 kJ mol–1, ΔS 0 53–60 J mol–1 K–1). For [Fe([9]aneN2S)2][ClO4]3 in the solid state [2.3 µB (300 K)–1.9 µB (4.2 K)] the magnetic data were fit to a simple model (H = –λL·S + µLz) to give the spin–orbit coupling constant (λ) of –260 ± 10 cm–1. The solid-state X-band EPR spectrum of [Fe([9]aneN2S)2][ClO4]3 revealed axial symmetry (g⊥ = 2.607, g|| = 1.599). Resolution of g⊥ into two components at Q-band frequencies indicated a rhombic distortion. The low-temperature single-crystal absorption spectra of [Fe([9]aneN2S)2][ClO4]2 and [Fe([9]aneNS2)2][ClO4]2 exhibited additional bands which resembled pseudo-tetragonal low-symmetry splitting of the parent octahedral 1A1g → 1T2g and 1A1g → 1T1g transitions. However, the magnitude of these splittings was too large, requiring 10Dq for the thioether donors to be significantly larger than for the amine donors. Instead, these bands were tentatively assigned to weak, low-energy S → FeII charge-transfer transitions. Above 200 K, thermal occupation of the high-spin 5T2g ground state resulted in observation of the 5T2g → 5Eg transition in the crystal spectrum of [Fe([9]aneN2S)2][ClO4]2. From a temperature-dependence study, the separation of the low-spin 1A1g and high-spin 5T2g ground states was approximately 1700 cm–1. The spectrum of the iron(III) complex [Fe([9]aneN2S)2][ClO4]3 is consistent with a low-spin d5 configuration.