L. B. Castro, A. S. de Castro
Eigenstates of a particle in a localized and unconfined harmonic potential well are investigated. Effects due to the variation of the potential parameters as well as certain results from asymptotic expansions are discussed.
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A new strategy for trapping quantum particles is presented, which behaves like an effective harmonic oscillator potential trap wherever is desired. The approach is based on harmonic contraction and expansion of the system around a fixed point (trapping point) at high frequencies. Analytical results are presented for an arbitrary potential and contrasted with numerical calculations for a quantum particle between two impenetrable walls. Similarly, making use of the analogy between quantum mechanics and optics, it is shown that an harmonically breathing waveguide lattice can be used to trap optic…
Ferromagnetic levitation and harmonic trapping of a milligram-scale Yttrium Iron Garnet sphere
本文在4 K下实现了0.3毫克钇铁石榴石球的被动磁悬浮与三维谐波囚禁，测得囚禁频率约600 Hz、Q值约10^3，并用三维有限元模拟定量验证，为磁性-力学-微波-光学耦合研究提供了新平台。
The time evolution of driven two-level systems in the far off-resonance regime is studied analytically. We obtain a general first-order perturbative expression for the time-dependent density operator which is applicable regardless of the coupling strength value. In the strong field regime, our perturbative expansion remains valid even when the far off-resonance condition is not fulfilled. We find that, in the absence of dissipation, driven two-level systems exhibit coherent population trapping in a certain region of parameter space, a property which, in the particular case of a symmetric doubl…
Continuous feedback protocols for cooling and trapping a quantum harmonic oscillator
本文基于量子Fokker-Planck主方程（QFPME）研究连续弱测量下的反馈冷却方案，分析了基于位置和/或动量测量的多种协议对谐振子的冷却与俘获效果，发现合适参数下可使其冷却至基态或接近基态，为量子测量与反馈提供了可解案例。
The Role of Singular Control in Frictionless Atom Cooling in a Harmonic Trapping Potential
研究通过奇异控制实现谐振子势阱中原子无摩擦冷却，同时最小化系统瞬态能量，并证明该控制是能量固定对偶问题的时间最优解。
A novel derivation of quantum propagator of a system described by a general quadratic Lagrangian is presented in the framework of Heisenberg equations of motion. The general corresponding density matrix is obtained for a derived quantum harmonic oscillator and a particle confined in a one dimensional Paul trap. Total mean energy, work and absorbed heat, Wigner function and excitation probabilities are found explicitly. The method presented here is based on the Heisenberg representation of position and momentum operators and can be generalized to a system consisting of a set of linearly interac…
Periodic Anderson model (PAM), where local electron orbitals interplay with itinerant electronic carriers, plays an essential role in our understanding on heavy fermion materials. Motivated by recent proposal of simulating Kondo lattice model (KLM) in terms of alkaline-earth metal atoms, we make a further step toward simulation of PAM, which includes crucial charge/valence fluctuation of local f-electron beyond purely low-energy spin fluctuation in KLM. To realize PAM, transition induced by suitable laser between electronic excited and ground state of alkaline-earth metal atoms ($^{1}S_{0}$$\r…
We analyze the dynamics of two atoms with a short-ranged pair interaction in a one-dimensional harmonic trap with time-dependent frequency. Our analysis is focused on two representative cases: (i) a sudden change of the trapping frequency from one value to another, and (ii) a periodic trapping frequency. In case (i), the dynamics of the interacting and the corresponding non-interacting systems turn out to be similar. In the second case, however, the interacting system can behave quite differently, especially close to parametric resonance. For instance, in the regions where such resonance occur…
Trapping microparticles in a structured dark focus
本文实验展示了暗焦点光镊对二氧化硅微球的稳定捕获与操控，通过功率谱和势能分析揭示其非谐势能景观，并探讨了在悬浮光力学和生物物理中的应用。
We study the performance of a quantum Otto cycle driven by trapping potentials of the form $V_t(x) \sim x^{2q}$. This family of potentials possesses a simple scaling property which allows for analytical insights into the efficiency and work output of the cycle. We show that, while both the mean work output and the efficiency of two Otto cycles in different trapping potentials can be made equal, the work probability distribution will still be strongly affected by the difference in structure of the energy levels. Lastly, we perform a comparison of quantum Otto cycles in various physically releva…
Recently predicted and observed Pauli crystals are structures formed by trapped ultracold non-interacting particles obeying Fermi statistics. The relative positions of the particles are determined by the trapping potential and the Pauli exclusion principle. Measuring all particles at once, their positions tend to be close to vertices of non-trivial polyhedrons. Similar shapes are found for systems of particles bound to the surface of a sphere.
Spatial and temporal evolution is studied of two powerful short laser pulses having different wavelengths and interacting with a dense three-level Lambda-type optical medium under coherent population trapping. A general case of unequal oscillator strengths of the transitions is considered. Durations of the probe pulse and the coupling pulse $T_{1,2}$ ($T_2>T_1$) are assumed to be shorter than any of the relevant atomic relaxation times. We propose analytical and numerical solutions of a self-consistent set of coupled Schrödinger equations and reduced wave equations in the adiabatic limit with …
We consider a system composed of a trapped atom and a trapped ion. The ion charge induces in the atom an electric dipole moment, which attracts it with an r^{-4} dependence at large distances. In the regime considered here, the characteristic range of the atom-ion interaction is comparable or larger than the characteristic size of the trapping potential, which excludes the application of the contact pseudopotential. The short-range part of the interaction is described in the framework of quantum-defect theory, by introducing some short-range parameters, which can be related to the s-wave scatt…
We study the role of quantum statistics in the performance of Otto cycles. First, we show analytically that the work distributions for bosonic and fermionic working fluids are identical for cycles driven by harmonic trapping potentials. Subsequently, in the case of non-harmonic potentials, we find that the interplay between different energy level spacings and particle statistics strongly affects the performances of the engine cycle. To demonstrate this, we examine three trapping potentials which induce different (single particle) energy level spacings: monotonically decreasing with the level n…
Frequency locking: a distinctive feature of the coherent population trapping and the stationarity effect
本研究探讨了相位调制用于频率稳定时，相干布居俘获在高频调制下保持最大误差信号斜率，而在低频调制下呈现平稳性效应。
We consider a strongly repulsive fermionic gas in a two-dimensional optical lattice confined by a harmonic trapping potential. To address the strongly repulsive regime, we consider the $t-J$ Hamiltonian. The presence of the harmonic trapping potential enables the stabilization of coexisting and competing phases. In particular, at low temperatures, this allows the realization of a d-wave superfluid region surrounded by purely (gapless) normal edges. Solving the Bogoliubov-de Gennes equations and comparing with the local density approximation, we show that the proximity to the Mott insulator is …
We consider a pair of atoms in an arbitrary trapping potential in the presence of magnetically tunable Feshbach resonance. We find the energy levels and occupation of the bound molecular states taking into account possible coupling between center of mass and relative motion induced by the trap. As a specific example we discuss the case of different atomic species in harmonic potential, where each atom feels different trapping frequency.
We study the creation of vortex states in a trapped Bose-Einstein condensate by a rotating force. For a harmonic trapping potential the rotating force induces only a circular motion of the whole condensate around the trap center which does not depend on the interatomic interaction. For the creation of a pure vortex state it is necessary to confine the atoms in an anharmonic trapping potential. The efficiency of the creation can be greatly enhanced by a sinusodial variation of the force's angular velocity. We present analytical and numerical calculations for the case of a quartic trapping poten…
We theoretically investigate the properties of two interacting ultracold highly magnetic atoms trapped in a one-dimensional harmonic potential. The atoms interact via an anisotropic long-range dipole-dipole interaction, which in one dimension effectively can be modeled by the contact interaction. We investigate the interplay of the external magnetic field, the spin-spin interaction, and the trapping potential and how they affect the magnetization of the system. We show the role of indistinguishability and symmetries in the dynamics by studying the time evolution of the observables that could b…
We investigate the properties of two interacting ultracold polar molecules described as distinguishable quantum rigid rotors, trapped in a one-dimensional harmonic potential. The molecules interact via a multichannel two-body contact potential, incorporating the short-range anisotropy of intermolecular interactions including dipole-dipole interaction. The impact of external electric and magnetic fields resulting in Stark and Zeeman shifts of molecular rovibrational states is also investigated. Energy spectra and eigenstates are calculated by means of the exact diagonalization. The importance a…
Stable magnetic levitation of soft ferromagnets for macroscopic quantum mechanics
提出利用磁场梯度和迈斯纳效应实现软铁磁体被动磁悬浮与三维捕获，实现高品质因子（$Q>10^8$）及宏观量子控制，为亚毫米尺度量子现象提供途径。
Precise understanding of the dynamics of trapped particles is crucial for nascent quantum technologies, including atomic clocks and quantum simulators. Here we present a framework to systematically include quantum effects arising from the mass-energy equivalence in harmonically trapped systems. We find that the mass-energy equivalence leads to squeezing, displacement and frequency changes of harmonic modes associated with different internal energies. The framework predicts new phenomena, notably, the existence of a lower bound to the fractional frequency shift in atomic clocks arising from the…
In our previous paper, we have investigated the thermodynamics of the quantum ultra-cold neutron gas trapped in the two-dimensional square-well potential on the Earth's gravitational field. We have pointed out that they have strong dependence on the shape of the trapping potential. In the present paper, we estimate the Fermi energy and the density distribution of the Fermi gas with two-dimensional harmonic oscillator potential, instead of the square-well potential. Then we discuss them in terms of the Fermi energy and the density distribution as compared with both of cases.
Self-induced Josephson oscillations and self-trapping in a supersolid dipolar quantum gas
本文从理论上证明谐波束缚偶极超固体可用广义约瑟夫森模型描述，并展现出包括宏观量子自俘获在内的标准约瑟夫森结阵列性质，为研究新型约瑟夫森结开辟了道路。
In this chapter we review the field of radio-frequency dressed atom trapping. We emphasise the role of adiabatic potentials and give simple, but generic models of electromagnetic fields that currently produce traps for atoms at microkelvin temperatures and below. The paper aims to be didactic and starts with general descriptions of the essential ingredients of adiabaticity and magnetic resonance. As examples of adiabatic potentials we pay attention to radio-frequency dressing in both the quadrupole trap and the Ioffe-Pritchard trap. We include a description of the effect of different choices o…
Motivated by the recent progress in cooling and trapping polar molecules, we present a simplified version of the rigorous contact pseudopotential for anisotropically-interacting polarized particles [A. Derevianko, Phys. Rev. A 67, 033607 (2003); Phys. Rev. A 72, 039901(E) (2005)]. The simplifications are carried out for a practically important case of harmonically confined particles described by sufficiently smooth wavefunctions. The resulting contact pseudo-potential depends on the K-matrix of the underlying scattering process and is represented as a sum over pairs of partial waves coupled by…
We consider a spin-orbit coupled system of particles in an external trap that is represented by a deformed harmonic oscillator potential. The spin-orbit interaction is a Rashba interaction that does not commute with the trapping potential and requires a full numerical treatment in order to obtain the spectrum. The effect of a Zeeman term is also considered. Our results demonstrate that variable spectral gaps occur as a function of strength of the Rashba interaction and deformation of the harmonic trapping potential. The single-particle density of states and the critical strength for superfluid…
The dynamics of the next quantum jump for a qubit [two level system] coupled to a readout resonator [damped driven harmonic oscillator] is calculated. A quantum mechanical treatment of readout resonator reveals non exponential short time behavior which could facilitate detection of the state of the qubit faster than the resonator lifetime.
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