Searcharxiv⌕ Search

arXiv subjects

Chengguang Bao

Publications and source records attributed to Chengguang Bao.

At least 19 recordsLinked to original sources
arXiv2025

A set of nearly good real numbers to specify the ground states associated with a Hamiltonian containing non-commutable terms and the effect of the odd-channel of a pair of different bosons emerging in multi-species systems

A distinguishing feature of multi-species boson systems is the appearance of the odd channel, in which the spins of two different bosons are coupled to an odd integer. Through exact numerical solutions of the Schrodinger equation for a medium-body cold system containing two kinds of spin-1 atoms, the effect of the odd channel on the ground state (GS) has been studied. It was found that the odd-channel causes two types of fluctuation (a mixing of various components). (i) coherent mixing, where all the components have the same sign. In this way, the probability of an odd-pair emerging in the spin-state would be smaller; thus, this way would be adopted by the GS when the odd channel is repulsive. (ii) cyclic mixing, where half selected components have the + sign while the other half have the - sign. In this way, the probability of an odd-pair is larger; thus, this way would be adopted by the GS when the odd channel is attractive. It was further found that the terms in the Hamiltonian are no longer all commutable. Accordingly, the spin of a single species S_X (X=A, B) is no longer conserved. However, its average \overline{S_X} is well defined. It turns out that S_X and \overline{S_X} vary with the strengths in a similar way. The former jumps step-by-step from a good quantum number (an even integer) to the next good quantum number, the latter jumps also in a step-by-step way, but from a "real number" to another well-separated "real number". Exactly speaking, each of these real numbers is not exactly a number but an interval with a very narrow width at the real axis. Thus, the GS can be specified by these real numbers. It was found that, when the strengths of the two intraspecies interactions are not remarkably different, and/or the particle numbers are larger, the widths of the intervals are narrower, the above picture holds more nicely, and the GS can be well-specified by these real numbers.

cond-mat.other↗
arXiv2017

Hyperfine state entanglement of spinor BEC and scattering atom

Condensate of spin-1 atoms frozen in a unique spatial mode may possess large internal degrees of freedom. The scattering amplitudes of polarized cold atoms scattered by the condensate are obtained with the method of fractional parentage coefficients that treats the spin degrees of freedom rigorously. Channels with scattering cross sections enhanced by square of atom number of the condensate are found. Entanglement between the condensate and the propagating atom can be established by the scattering. The entanglement entropy is analytically obtained for arbitrary initial states. Our results also give hint for the establishment of quantum thermal ensembles in the hyperfine space.

cond-mat.quant-gas↗
arXiv2013

Spin-thermodynamics of cold spin-1 atoms decoupled from spatial modes

We study the thermodynamic properties of cold spin-1 atoms with a fixed magnetization M and decoupled from spatial modes. Three temperature domains are found: (0, T1) is a domain of second condensation, namely, both the spatial and spin degrees of freedom are frozen; (T1, T2) is a T - sensitive domain, where the internal energy U \propto T, entropy SE \propto log T, and U/kBT is always less than 3/2; (T2, T3) is the third domain with a maximum entropy. When T is higher than T3, the spatial modes can not be neglected. The appearance of these domains originates from the two gaps: (i) The gap between the ground state and the first excited state, and (ii) the gap between the highest spin-state without spatial excitation and the lowest state with a spatial mode excited. These two gaps are crucial to the low temperature physics and they can be tuned.

cond-mat.stat-mech↗
arXiv2013

A 2-level system of cold sodium atoms with high and tunable susceptibility against the magnetic field

A 2-level spin-system of cold sodium atoms is proposed. Both the cases that the system has arrived at thermo-equilibrium and is in the early stage of evolution have been studied. This system is inert to the magnetic field $B$ in general but very sensitive in a narrow domain around $B=B_0$, where $B_0$ can be predicted and is tunable. A characteristic constant $γ=0.278466$ dedicated to various 2-level systems is found, and leads to a upper limit for the internal energy $U$ of the whole system so that $U\leqγk_B T$. This limit is considerably lower than the energy assigned to the spatial motion of only a single particle. Under thermo-equilibrium, the populations of spin-components measured at distinct $T$ converge to a fixed value when $B=B_0$. The period and amplitude of population oscillation are found to be seriously affected by the special sensitivity against $B$. Rich messages on the dynamic parameters could be obtained via experimental measurements of these systems.

physics.atom-ph↗
arXiv2013

Universal prohibited zones in the coordinate space of few-body systems

In some special zones of the high-dimensional coordinate space of few-body systems with identical particles, the operation of an element (or a product of elements) of the symmetry groups of the Hamiltonian on a quantum state might be equivalent to the operation of another element. Making use of the matrix representations of the groups, the equivalence leads to a set of homogeneous linear equations imposing on the wave functions. When the matrix of these equations is non-degenerate, the wave functions will appear as nodal surfaces in these zones. In this case, these zones are prohibited. In this paper, tightly bound 4-boson systems with three types of interaction have been studied analytically and numerically. The existence of the universal prohibited zones has been revealed, and their decisive effect on the structures of the eigenstates is demonstrated.

physics.atom-ph↗
arXiv2012

Universality in tightly bound 3-boson systems

The effects of two distinct operations of the elements of the symmetry groups of a Hamiltonian on a quantum state might be equivalent in some specific zones of coordinate space. Making use of the matrix representations of the groups, the equivalence leads to a set of homogeneous linear equations imposing on the wave functions. When the matrix of the equations is non-degenerate, the wave functions will appear as nodal surfaces in these zones. Therefore, the equivalence leads to the existence of inherent nodal structure in the quantum states. In this paper, trapped 3-boson systems with different types of interactions are studied. The structures of the tightly bound eigenstates have been analyzed systematically. The emphasis is placed to demonstrate the universality arising from the common inherent nodal structures.

quant-ph↗
arXiv2011

Elementary modes of excitation caused by the quadratic Zeeman term and the sensitivity of spin structures of small spin-2 condensates against the magnetic field

The response of spin-2 small condensates to an external magnetic field $B$ is studied. The parameters of the interaction are considered as variable. The emphasis is placed on clarifying the modes of excitation caused by the quadratic Zeeman term. The theoretical method used is beyond the mean field theory. A set of eigenstates with the $U(5)\supset SO(5)\supset SO(3)$ symmetry is introduced to facilitate the analysis. To obtain a quantitative evaluation on the response, the fidelity susceptibility and the $B$ -dependent average populations of spin-components have been calculated. Mostly the particle number N=30 is assumed. The effect with a larger or smaller $N$ is also considered. It was found that the sensitivity of the response depends strongly both on the interaction and on the inherent symmetry.

cond-mat.quant-gas↗
arXiv2011

Sensitivity of spin structures of small spin-1 condensates against a magnetic field studied beyond the mean field theory

The spin structures of small spin-1 condensates ($N\leq 1000$) under a magnetic field $B$ has been studied beyond the mean field theory (MFT). Instead of the spinors, the many body spin-eigenstates have been obtained. We have defined and calculated the spin correlative probabilities to extract information from these eigenstates. The correlation coefficients and the fidelity susceptibility have also been calculated. Thereby the details of the spin-structures responding to the variation of $B$ can be better understood. In particular, from the correlation coefficients which is the ratio of the 2-body probability to the product of two 1-body probabilities, strong correlation domains (SCD) of $B$ are found. The emphasis is placed on the sensitivity of the condensates against $B$. No phase transitions in spin-structures are found. However, abrupt changes in the derivatives of observables (correlative probabilities) are found in some particular domains of $B$. In these domains the condensates are highly sensitive to $B$. The effect of temperature is considered. The probabilities defined in the paper can work as a bridge to relate theories and experiments. Therefore, they can be used to discriminate various spin-structures and refine the interactions.

cond-mat.other↗
arXiv2010

Repeating head-on collisions in an optical trap and the evaluation of spin-dependent interactions among neutral particles

A dynamic process of repeating collisions of a pair of trapped neutral particles with weak spin-dependent interaction is designed and studied. Related theoretical derivation and numerical calculation have been performed to study the inherent coordinate-spin and momentum-spin correlation. Due to the repeating collisions the effect of the weak interaction can be accumulated and enlarged, and therefore can be eventually detected. Numerical results suggest that the Cr-Cr interaction, which has not yet been completely clear, could be thereby determined. The design can be in general used to determine various interactions among neutral atoms and molecules, in particular for the determination of very weak forces.

cond-mat.other↗
arXiv2010

Repeating 3-body collisions in a trap and the evaluation of interactions of neutral particles

A model of a device is proposed and related theoretical calculation is performed to study the weak interactions among neutral atoms and molecules. In this model 3-body collisions among the neutral particles occur repeatedly in a trap. Results of calculation demonstrate that information on interaction can be obtained by observing the time-dependent densities of the system.

cond-mat.other↗
arXiv2010

Two-body scattering in a trap and a special periodic phenomenon sensitive to the interaction

Two-body scattering of neutral particles in a trap is studied theoretically. The control of the initial state is realized by using optical traps. The collisions inside the trap occur repeatedly; thereby the effect of interaction can be accumulated. Two periodic phenomena with a shorter and a much longer period, respectively, are found. The latter is sensitive to the interaction. Instead of measuring the differential cross section as usually does, the measurement of the longer period and the details of the periodic behavior might be a valid source of information on weak interactions among neutral particles.

cond-mat.other↗
arXiv2010

Periodic giant-persistent current in sharp pulses on a ring

We show here a mesoscopic device based on a narrow ring containing an electron. In the device, an amount of energy is stored in advance. Similar to the pendulum, an exact periodic motion of the electron is thereby initiated afterward. The motion appears as a series of sharp pulses, and is in nature different from the well known Aharonov-Bohm (A-B) oscillation. In particular, the pulses of current can be tuned to be very strong (say, more than two orders stronger than the usual A-B current). Related theory and numerical results are presented.

cond-mat.other↗
arXiv2009

Strong spin-oscillation of small spin-1 condensates caused by an inclined weak magnetic field

When a magnetic field is applied along a direction deviated from the quantization $Z$-axis, the conservation of total magnetization holds no more. In this case the inclined field can cause a strong spin-evolution via the linear Zeeman term even the field is as weak as a percentage of $mG$. An approach beyond the mean field theory is proposed to study the evolution of small $^{87}$Rb condensates under the weak inclined fields. The time-dependent populations of spin-components are given in analytical forms. The evolution is found to be highly sensitive to the magnitude and direction of the field.

cond-mat.other↗
arXiv2009

Spin-structures of N-boson systems with nonzero spins - an analytically solvable model with pairing force

A model is proposed to study the possible pairing structures of N-boson systems with nonzero spin. Analytical solutions have been obtained. The emphasis is placed on the spin-structures of ground states with attractive or repulsive pairing force, and with or without the action of a magnetic field. A quantity (an analogue of the two-body density function) is defined to study the spin-correlation between two bosons in N-body systems. The excitation of the system has also been studied.

cond-mat.other↗
arXiv2009

Modification of spin mixing of spinor BEC by cavity QED coupling

Dressed states of spinor Bose-Einstein condensates of spin-1 atoms coupling with optical cavity modes with far off resonance frequency are investigated. The exact solution of time evolution of population of spin component is derived, and the numerical result shows that the evolution is different from spin mixing without the coupling. Due to the coupling with the atoms, the photon state also evolute to different optical cavity modes.

physics.atm-clus↗
arXiv2008

Mesoscopic oscillator in U-shape with giant persistent current

A mesoscopic oscillator in U-shape has been proposed and studied. Making use of a magnetic flux together with a potential of confinement, the electron contained in the oscillator has been localized initially and an amount of energy has been thereby stored. Then a sudden cancellation of both the potential and the flux may cause an initial current which initiates a periodic motion of the electron from one end of the U-oscillator to the opposite end, and repeatedly. The period is adjustable. The current associated with the periodic motion can be tuned very strong (say, more than two orders larger than the current of the usual Aharonov-Bohm oscillation). Related theory and numerical results are presented.

cond-mat.mes-hall↗