Many-particle States Research Articles

Topological Interface Engineering and Defect Crossing in Ultracold Atomic Gases

We propose an experimentally feasible scheme for topological interface engineering and show how it can be used for studies of dynamics of topologically nontrivial interfaces and perforation of defects and textures across such interfaces. The method makes use of the internal spin structure of the atoms together with locally applied control of interaction strengths to create many-particle states with highly complex topological properties. In particular, we consider a constructed coherent interface between topologically distinct phases of spinor Bose-Einstein condensates.

Bose–Hubbard model on two-dimensional line graphs

We construct a basis for the many-particle ground states of the positive hopping Bose–Hubbard model on line graphs of finite 2-connected planar bipartite graphs at sufficiently low filling factors. The particles in these states are localized on non-intersecting vertex-disjoint cycles of the line graph which correspond to non-intersecting edge-disjoint cycles of the original graph. The construction works up to a critical filling factor at which the cycles are close-packed.

Macroscopic quantum superpositon states of two-component Bose-Einstein condensates

We examine a two-component Bose-Einstein condensate in a double-well potential. We propose a model for the creation of many-particle macroscopic quantum superposition states. The effect of dissipation on the formation of these states is also investigated with the Monte-Carlo wavefunction technique.

A computer program for two-particle intrinsic coefficients of fractional parentage

A Fortran 90 program CESOS for the calculation of the two-particle intrinsic coefficients of fractional parentage for several j-shells with isospin and an arbitrary number of oscillator quanta (CESOs) is presented. The implemented procedure for CESOs calculation consistently follows the principles of antisymmetry and translational invariance. The approach is based on a simple enumeration scheme for antisymmetric many-particle states, efficient algorithms for calculation of the coefficients of fractional parentage for j-shells with isospin, and construction of the subspace of the center-of-mass Hamiltonian eigenvectors corresponding to the minimal eigenvalue equal to 3/2 (in ℏω). The program provides fast calculation of CESOs for a given particle number and produces results possessing small numerical uncertainties. The introduced CESOs may be used for calculation of expectation values of two-particle nuclear shell-model operators within the isospin formalism. Program summaryProgram title: CESOSCatalogue identifier: AELT_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELT_v1_0.htmlProgram obtainable from: CPC Program Library, Queenʼs University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 10 932No. of bytes in distributed program, including test data, etc.: 61 023Distribution format: tar.gzProgramming language: Fortran 90Computer: Any computer with a Fortran 90 compilerOperating system: Windows XP, LinuxRAM: The memory demand depends on the number of particles A and the excitation energy of the system Ex. Computation of the A=6 particle system with the total angular momentum J=0 and the total isospin T=1 requires around 4 kB of RAM at Ex=0,∼3 MB at Ex=3, and ∼172 MB at Ex=5.Classification: 17.18Nature of problem: The code CESOS generates a list of two-particle intrinsic coefficients of fractional parentage for several j-shells with isospin.Solution method: The method is based on the observation that CESOs may be obtained by diagonalizing the center-of-mass Hamiltonian in the basis set of antisymmetric A-particle oscillator functions with singled out dependence on Jacobi coordinates of two last particles and choosing the subspace of its eigenvectors corresponding to the minimal eigenvalue equal to 3/2.Restrictions: One run of the code CESOS generates CESOs for one specified set of (A,Ex,J,T) values only. The restrictions on the (A,Ex,J,T) values are completely determined by the restrictions on the computation of the single-shell CFPs and two-particle multishell CFPs (GCFPs) [1]. The full sets of single-shell CFPs may be calculated up to the j=9/2 shell (for any particular shell of the configuration); the shell with j⩾11/2 cannot get full (it is the implementation constraint). The calculation of GCFPs is limited by A<86 when Ex=0 (due to the memory constraints); small numbers of particles allow significantly higher excitations. Any allowed values of J and T may be chosen for the specified values of A and Ex. The complete list of allowed values of J and T for the chosen values of A and Ex may be generated by the GCFP program – CPC Program Library, Catalogue Id. AEBI_v1_0. The actual scale of the CESOs computation problem depends strongly on the magnitude of the A and Ex values. Though there are no limitations on A and Ex values (within the limits of single-shell CFPs and multishell CFPs calculation), however the generation of corresponding list of CESOs is the subject of available computing resources. For example, the computing time of CESOs for A=6, JT=10 at Ex=5 took around 14 hours. The system with A=11, JT=1/23/2 at Ex=2 requires around 15 hours. These computations were performed on Pentium 3 GHz PC with 1 GB RAM [2].Unusual features: It is possible to test the computed CESOs without saving them to a file. This allows the user to learn their number and approximate computation time and to evaluate the accuracy of calculations.Additional comments: The program CESOS uses the code from GCFP program for calculation of the two-particle multishell coefficients of fractional parentage.Running time: It depends on the size of the problem. The A=6 particle system with the JT=01 took around 31 seconds on Pentium 3 GHz PC with 1 GB RAM at Ex=3 and about 2.6 hours at Ex=5.

A solution for tensor reduction of one-loop N-point functions with [formula omitted

Collisions at the LHC produce many-particle final states, and for precise predictions the one-loop N-point corrections are needed. We study here the tensor reduction for Feynman integrals with N⩾6. A general, recursive solution by Binoth et al. expresses N-point Feynman integrals of rank R in terms of (N−1)-point Feynman integrals of rank (R−1) (for N⩾6). We show that the coefficients can be obtained analytically from suitable representations of the metric tensor. Contractions of the tensor integrals with external momenta can be efficiently expressed as well. We consider our approach particularly well suited for automatization.

Nonlinear interference in a mean-field quantum model

Using similar nonlinear stationary mean-field models for both a 2D axisymmetrical Bose-Einstein Condensate and an electron pair in a parabolic trap, we propose to describe the original many-particle ground state as a one-particle mixed state (in contrast to a pure state), i.e. as a statistical ensemble of several one-particle quantum states. These quantum states are the eigenfunctions of the corresponding stationary nonlinear Schrödinger equation (hence called “nonlinear eigenstates”). Due to their nonlinearity, they are not orthogonal. Therefore, taking the simple example of a two-level system, we show that each of these two nonlinear eigenstates |i⟩ and |j⟩ occurs with a probability (or statistical weight) that is defined by their non-orthogonality ⟨i|j⟩ 0. We give the corresponding density matrix. We search for physical grounds in the interpretation of our two main results, namely, a quantum-classical nonlinear transition and the interference between two “nonlinear eigenstates”.

Optically induced conical intersections in traps for ultracold atoms and molecules

We show that conical intersections can be created in laboratory coordinates by dressing a parabolic trap for ultracold atoms or molecules with a combination of optical and static magnetic fields. The resulting ring trap can support single-particle states with half-integer rotational quantization and many-particle states with persistent flow. Two well-separated atomic or molecular states are brought into near resonance by an optical field and tuned across each other with an inhomogeneous magnetic field. Conical intersections occur at the nodes in the optical field.

Quantum level engineering for Aharonov-Bohm caging in the presence of electron-electron interactions

Aharonov-Bohm (AB) cages are finite regions of a quantum network where single-particle eigenstates remain extremely localized for certain values of an applied magnetic field. Electron-electron interactions partially destroy the single-particle localization by the generation of extended many-particle states. We address the effects of on-site potentials on the AB localization phenomenon in a diamond-shaped quasi-one-dimensional bipartite chain, and show that field-induced AB cages can effectively persist in the presence of electron-electron interactions.

Supercurrent through a multilevel quantum dot close to singlet-triplet degeneracy

We investigate two serially aligned quantum dots in the molecular regime of large tunnel couplings $t$. A Zeeman field $B$ is used to tune the energy difference of singlet and triplet spin configurations. Attaching this geometry to BCS source and drain leads with gap $\ensuremath{\Delta}$ and phase difference $\ensuremath{\varphi}$ gives rise to an equilibrium supercurrent $J$. To compute $J$ in the presence of Coulomb interactions $U$ between the dot electrons, we employ the functional renormalization group (FRG). For $B\ensuremath{\approx}t$, where the singlet and (one out of a) triplet spin states are equal in energy, the current exhibits characteristics of a 0-$\ensuremath{\pi}$ transition similar to a single impurity. Its magnitude in the $\ensuremath{\pi}$ phase, however, jumps discontinuously at $B=t$, being smaller on the triplet side. By exploiting the flexibility of the FRG, we demonstrate that this effect is generic and calculate $J$ for realistic experimental parameters $\ensuremath{\Delta}$, $U$, and gate voltages $\ensuremath{\epsilon}$. To obtain a more thorough understanding of the discontinuity, we analytically treat the limit $\ensuremath{\Delta}=\ensuremath{\infty}$, where one can access the exact many-particle states. Finally, carrying out perturbation theory in the dot-lead couplings substantiates the intuitive picture that Cooper-pair tunneling is favored by a singlet spin configuration while inhibited by a triplet one.

Creation of collective many-body states and single photons from two-dimensional Rydberg lattice gases

The creation of collective many-body quantum states from a two-dimensional lattice gas of atoms is studied. Our approach relies on the van der Waals interaction that is present between alkali metal atoms which are laser excited to high-lying Rydberg s-states. We focus on a regime in which the laser driving is strong compared to the interaction between Rydberg atoms. Here energetically low-lying many-particle states can be calculated approximately from a quadratic Hamiltonian. The potential usefulness of these states as a resource for the creation of deterministic single-photon sources is illustrated. The properties of these photon states are determined from the interplay between the particular geometry of the lattice and the interatomic spacing.

Elimination the centre-of-mass motion in the nuclear shell-model with isospin

An efficient procedure for large-scale calculations of the two-particle translational invariant coefficients of fractional parentage (CESO’s) for several j-shells with isospin is presented. The approach is based on a simple enumeration scheme for antisymmetric many-particle states and efficient algorithms for calculation of the coefficients of fractional parentage for a single j-shell and several j-shells with isospin. The CESO’s may be obtained by diagonalizing the centre-of-mass Hamiltonian in the basis set of antisymmetric A-particle oscillator functions with singled out dependence on intrinsic coordinates of two last particles and choosing the subspace of its eigenvectors corresponding to the minimal eigenvalue equal to 3/2. An arbitrary number of oscillator quanta can be involved. The characteristics of the introduced CESO’s basis are investigated.

Time-resolved high-temperature detection with single charge resolution of holes tunneling into many-particle quantum dot states

We demonstrate detection of many-particle hole states in InAs/GaAs quantum dots with single charge resolution up to a temperature of 75 K. Capacitance-voltage measurements as well as time-resolved current measurements in an adjacent two-dimensional hole gas are used to determine the emission and capture time constants from 4 K up to 130 K. A transition from pure tunneling to thermally assisted tunneling is observed with increasing temperature. An equivalent circuit model gives access to the energy level splittings of the many-particle hole states and explains the broadening of the peaks at higher temperatures.

Theoretical Analysis of the Anomalous Spectral Splitting of Tetracene in 4He Droplets

We present a theoretical analysis of the electronic absorption spectra of tetracene in (4)He droplets based on many-body quantum simulations. Using the path integral ground state approach, we calculate one- and two-body reduced density matrices of the most strongly localized He atoms near the molecule surface and use these to investigate the helium ground-state quantum coherence and correlations when tetracene is in its electronic ground and excited states. We identify a trio of quasi-one-dimensional, strongly localized atoms adsorbed along the long axis of the molecule that show some quantum coherence among themselves but far less with the remaining solvating helium. We evaluate the single-particle natural orbitals of the localized He atoms by diagonalization of the one-body density matrix and use these to construct single- and many-particle solvating helium basis states with which the zero-phonon spectral features of the tetracene-(4)He(N) absorption spectrum are then calculated. The absorption spectrum resulting from the three-body density matrix for the strongly bound trio of helium atoms is in very good agreement with the experimental data, accounting quantitatively for the anomalous splitting of the zero-phonon line [Hartmann, M.; Lindinger, A.; Toennies, J. P.; Vilesov, A. F. Chem. Phys. 1998, 239, 139; Krasnokutski, S.; Rouillé, G.; Huisken, F. Chem. Phys. Lett. 2005, 406, 386]. Our results indicate that the combination of strong localization and the quasi-one-dimensional nature of trios of helium atoms adsorbed along the long axis of tetracene leads to a quantum coherent, yet highly correlated ground state for the helium density closest to the molecule. The spectroscopic analysis shows that this feature accounts quantitatively for the anomalous splittings and hitherto unexplained fine structure observed in the absorption spectra of tetracene and suggests that it may be responsible for the corresponding zero-phonon splittings in other quasi-one-dimensional planar aromatic molecules.

Anomalous local coordination, density fluctuations, and void statistics in disordered hyperuniform many-particle ground states

We provide numerical constructions of one-dimensional hyperuniform many-particle distributions that exhibit unusual clustering and asymptotic local number density fluctuations growing more slowly than the volume of an observation window but faster than the surface area. Hyperuniformity, defined by vanishing infinite-wavelength local density fluctuations, provides a quantitative metric of global order within a many-particle configuration and signals the onset of an "inverted" critical point in which the direct correlation function becomes long ranged. By targeting a specified form of the structure factor at small wavenumbers (S(k)~k(α) for 0<α<1) using collective density variables, we are able to tailor the form of asymptotic local density fluctuations while simultaneously measuring the effect of imposing weak and strong constraints on the available degrees of freedom within the system. This procedure is equivalent to finding the (possibly disordered) classical ground state of an interacting many-particle system with up to four-body interactions. Even in one dimension, the long-range effective interactions induce clustering and nontrivial phase transitions in the resulting ground-state configurations. We provide an analytical connection between the fraction of constrained degrees of freedom within the system and the disorder-order phase transition for a class of target structure factors by examining the realizability of the constrained contribution to the pair correlation function. Our results explicitly demonstrate that disordered hyperuniform many-particle ground states, and therefore also point distributions, with substantial clustering can be constructed. We directly relate the local coordination structure of our point patterns to the distribution of the void space external to the particles, and we provide a scaling argument for the configurational entropy (analogous to spin-frustated system) of the disordered ground states. By emphasizing the intimate connection between geometrical constraints on the particle distribution and structural regularity, our work has direct implications for higher-dimensional systems, including an understanding of the appearance of hyperuniformity and quasi-long-range pair correlations in maximally random strictly jammed packings of hard spheres.

Magnetoluminescence from trion and biexciton in type-II quantum dot

We theoretically investigate optical Aharonov-Bohm (AB) effects on trion and biexciton in the type-II semiconductor quantum dots, in which holes are localized near the center of the dot, and electrons are confined in a ring structure formed around the dot. Many-particle states are calculated numerically by the exact diagonalization method. Two electrons in trion and biexciton are strongly correlated to each other, forming a Wigner molecule. Since the relative motion of electrons are frozen, the Wigner molecule behaves as a composite particle whose mass and charges are twice those of an electron. As a result, the period of AB oscillation for trion and biexciton becomes h/2e as a function of magnetic flux penetrating the ring. We find that the magnetoluminescence spectra from trion and biexciton change discontinuously as the magnetic flux increases by h/2e.PACS: 71.35.Ji, 73.21.-b, 73.21.La, 78.67.Hc

Transport spectroscopy of non-equilibrium many-particle spin states in self-assembled quantum dots

Self-assembled quantum dots (QDs) are prominent candidates for solid-state quantum information processing. For these systems, great progress has been made in addressing spin states by optical means. In this study, we introduce an all-electrical measurement technique to prepare and detect non-equilibrium many-particle spin states in an ensemble of self-assembled QDs at liquid helium temperature. The excitation spectra of the one- (QD hydrogen), two- (QD helium) and three- (QD lithium) electron configuration are shown and compared with calculations using the exact diagonalization method. An exchange splitting of 10 meV between the excited triplet and singlet spin states is observed in the QD helium spectrum. These experiments are a starting point for an all-electrical control of electron spin states in self-assembled QDs above liquid helium temperature.

Ultrafast charge separation driven by differential particle and hole mobilities

The process of a local excitation evolving into an intramolecular charge-separated state is followed and compared for several systems by directly simulating the time propagation of the electronic wavefunction. The wavefunction and Hamiltonian are handled using the extended second-order algebraic diagrammatic construction (ADC(2)-x), which explicitly accounts for electron correlation in the dynamic many-particle state. The details of the charge separation can be manipulated according to the chemical composition of the system; atoms which dope the conjugated system with either particles or holes are shown to effect whether the particle or hole is more mobile. Initially, the charges oscillate between the ends of linear molecules (with different rates), separating periodically, but, at long times, both charges tend to spread over the whole molecule. Charge separation is also shown to occur for asymmetric systems, where it may eventually be experimentally feasible to excite a localized resonance (nonstationary state) on one end of the molecule preferentially and follow the ensuing dynamics.

A description of the evolution of quantum states by means of the kinetic equation

We develop a rigorous formalism for describing the evolution of states of quantum many-particle systems in terms of a one-particle density operator. For initial states which are specified in terms of a one-particle density operator, the equivalence of the description of the evolution of quantum many-particle states by the Cauchy problem of the quantum Bogolyubov–Born–Green–Kirkwood–Yvon hierarchy, and by the Cauchy problem of the generalized quantum kinetic equation, together with a sequence of explicitly defined functionals of a solution of a stated kinetic equation, is established in the space of trace-class operators. The links between the specific quantum kinetic equations with the generalized quantum kinetic equation are discussed.

Nonlinear atom interferometer surpasses classical precision limit

Interference is fundamental to wave dynamics and quantum mechanics. The quantum wave properties of particles are exploited in metrology using atom interferometers, allowing for high-precision inertia measurements. Furthermore, the state-of-the-art time standard is based on an interferometric technique known as Ramsey spectroscopy. However, the precision of an interferometer is limited by classical statistics owing to the finite number of atoms used to deduce the quantity of interest. Here we show experimentally that the classical precision limit can be surpassed using nonlinear atom interferometry with a Bose-Einstein condensate. Controlled interactions between the atoms lead to non-classical entangled states within the interferometer; this represents an alternative approach to the use of non-classical input states. Extending quantum interferometry to the regime of large atom number, we find that phase sensitivity is enhanced by 15 per cent relative to that in an ideal classical measurement. Our nonlinear atomic beam splitter follows the 'one-axis-twisting' scheme and implements interaction control using a narrow Feshbach resonance. We perform noise tomography of the quantum state within the interferometer and detect coherent spin squeezing with a squeezing factor of -8.2 dB (refs 11-15). The results provide information on the many-particle quantum state, and imply the entanglement of 170 atoms.

Calculating the energy spectrum and electronic structure of two holes in a pair of strained Ge/Si coupled quantum dots

We theoretically investigate the energy spectrum and electronic structure of two vertically stacked Ge/Si quantum dots loaded with a pair of interacting holes, and study the dependence of basic physical characteristics on dot size and interdot separation. In particular, we focus on the splitting of the lowest spin singlet and triplet states and spatial correlations between holes. Here the term ``spin'' is rather an index for two Kramers degenerate states. The two holes are treated by six-band $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ calculations combined with the configuration-interaction model taking into account the realistic situation when both Si matrix and Ge nanoclusters are inhomogeneously strained. It is shown that asymmetry of strain distribution and spin-orbit coupling of the valence band introduce characteristic features in both single- and many-particle hole states, which are not captured by the usual one-band heavy-hole approximation. We find a level anticrossing between the lowest singlet and triplet states with a zero anticrossing energy gap as a function of interdot spacing. It is demonstrated that the level anticrossing between many-particle states is accompanied by a level crossing between single-particle bonding and antibonding molecular orbitals. We argue that both phenomena of level crossing and anticrossing originate from the asymmetry-induced localization of single-particle hole wave functions on different dots. Above a certain dot separation, the Mott-type delocalized-to-localized transition for the many-particle hole states is observed. We show that the transition is caused by the combined action of correlations and strain asymmetry.