Anharmonic Trap Research Articles

Quench dynamics of a Tonks-Girardeau gas in one dimensional anharmonic trap

The quench dynamics of strongly interacting bosons on quartic and sextic traps are studied by exactly solving the time-dependent many-boson Schrödinger equation numerically. The dynamics are addressed by the key measures of one-body density in conjugate space and information entropy. For both cases, rich many-body dynamics are exhibited and the loss of the Bose–Fermi oscillation in the Tonks–Girardeau limit is also attributed.

Guided-wave Sagnac atom interferometer with large area and multiple orbits

We describe a matter-wave Sagnac interferometer using Bose condensed atoms confined in a time-orbiting potential trap. Compared to our previous implementation [Moan et al., Phys. Rev. Lett. 124, 120403 (2020)], our new apparatus provides better thermal stability, improved optical access, and reduced trap anharmonicity. The trapping field can be adjusted to compensate for small tilts of the apparatus in gravity. These features enable operation with an effective Sagnac area of 4 mm2 per orbit, and we observe interference with 25% visibility after two orbits at a total interrogation time of 0.6 s. Long-term measurements indicate a phase stability of 0.2 rad or better.

Optimal work fluctuations for finite-time and weak processes.

The optimal protocols for the irreversible work achieve their maximum usefulness if their work fluctuations are the smallest ones. In this work, for classical and isothermal processes subjected to finite-time and weak drivings, I show that the optimal protocol for the irreversible work is the same for the variance of work. This conclusion is based on the fluctuation-dissipation relation W[over ¯]=ΔF+βσ_{W}^{2}/2, extended now to finite-time and weak drivings. To illustrate it, I analyze a white-noise overdamped Brownian motion subjected to an anharmonic stiffening trap for fast processes. By contrast with the already known results in the literature for classical systems, the linear-response theory approach of the work probabilistic distribution is not a Gaussian reduction.

Ground states of attractive Bose gases in rotating anharmonic traps

This paper is concerned with ground states of attractive Bose gases confined in an anharmonic trap V(x)=ω(|x|2+k|x|4) rotating at the velocity Ω>0, where ω>0 denotes the trapping frequency, and k>0 represents the strength of the quartic term. It is known that for any Ω>0, ground states exist in such traps if and only if 0<a<a⁎, where a⁎:=‖Q‖22 and Q>0 is the unique positive solution of ΔQ−Q+Q3=0 in R2. By analyzing the refined energies and expansions of ground states, we prove that there exists a constant C>0, independent of 0<a<a⁎, such that ground states do not have any vortex in the region R(a):={x∈R2:|x|≤C(a⁎−a)−1−6β20} as a↗a⁎, for the case where ω=3Ω24, k=16, and Ω=C0(a⁎−a)−β varies for some β∈[0,16) and C0>0.

Spectral properties and exact solutions for Rabi-coupled noninteracting fermions in a spin-dependent anharmonic trapping potential

We investigate the effect of spin-motion coupling on the spectral properties of Rabi-coupled noninteracting fermions in a spin-dependent harmonic trapping potential plus an anharmonic term. It is shown that when the spin-motion coupling becomes strong, fermions tend to stay in one of the two components. In the limit of the strong spin-motion coupling, the entire energy spectrum exhibits a sequence of near degeneracy. In particular, in the case of the sextic anharmonic term, the system admits the exact analytical energies and wave functions of the bound states for an infinite number of the specific parameter conditions. The properties of the energy spectrum have also been discussed on basis of these obtained exact analytical solutions.

Superconducting Microsphere Magnetically Levitated in an Anharmonic Potential with Integrated Magnetic Readout

Magnetically levitated superconducting microparticles offer a promising path to quantum experiments with picogram to microgram objects. In this work, we levitate a 700ng $\sim 10^{17}$amu superconducting microsphere in a magnetic chip trap in which detection is integrated. We measure the particle's center-of-mass motion using a DC-SQUID magnetometer. The trap frequencies are continuously tunable between 30 and 160 Hz and the particle remains stably trapped over days in a dilution refrigerator environment. We characterize motional-amplitude-dependent frequency shifts, which arise from trap anharmonicities, namely Duffing nonlinearities and mode couplings. We explain this nonlinear behavior using finite element modelling of the chip-based trap potential. This work constitutes a first step towards quantum experiments and ultrasensitive inertial sensors with magnetically levitated superconducting microparticles.

Anharmonicity-induced phase transition of spin–orbit coupled Bose–Einstein condensates

In the mean-field framework, using variational analysis and numerical simulation, we investigate the effect of anharmonic trap and atomic interaction on the ground-state phases of spin-orbit (SO) coupled Bose–Einstein condensates (BECs) in the harmonic plus quartic potential. Then, the Gaussian wave function is selected to predict the analytical conditions of the phase transition boundary of the SO coupled BECs by using the variational method. We found that the anharmonicity of the external potential induces the SO coupled BECs to undergo a phase transition between the zero-momentum phase and plane-wave phase, which is more pronounced in the cases of weak harmonic potential or strong interspecies interaction. Since the potential energy of the system modified by anharmonicity competes with other energies of the system, the anharmonicity changes the critical SO coupling strength and Raman coupling strength when the phase transition occurs. At the same time, the critical anharmonic coefficients are also affected by interspecies interaction and harmonic potential. Finally, the correctness of the theoretical results is verified by numerical simulation of the Gross-Pitaevskii equation.

Mechanochemical Synthesis of Sustainable Ternary and Quaternary Nanostructured Cu2SnS3, Cu2ZnSnS4, and Cu2ZnSnSe4 Chalcogenides for Thermoelectric Applications

Copper-based chalcogenides have emerged as promising thermoelectric materials due to their high thermoelectric performance, tunable transport properties, earth abundance and low toxicity. We have presented an overview of experimental results and first-principal calculations investigating the thermoelectric properties of various polymorphs of Cu2SnS3 (CTS), Cu2ZnSnS4 (CZTS), and Cu2ZnSnSe4 (CZTSe) synthesized by high-energy reactive mechanical alloying (ball milling). Of particular interest are the disordered polymorphs of these materials, which exhibit phonon-glass-electron-crystal behavior-a decoupling of electron and phonon transport properties. The interplay of cationic disorder and nanostructuring leads to ultra-low thermal conductivities while enhancing electronic transport. These beneficial transport properties are the consequence of a plethora of features, including trap states, anharmonicity, rattling, and conductive surface states, both topologically trivial and non-trivial. Based on experimental results and computational methods, this report aims to elucidate the details of the electronic and lattice transport properties, thereby confirming that the higher thermoelectric (TE) performance of disordered polymorphs is essentially due to their complex crystallographic structures. In addition, we have presented synchrotron X-ray diffraction (SR-XRD) measurements and ab initio molecular dynamics (AIMD) simulations of the root-mean-square displacement (RMSD) in these materials, confirming anharmonicity and bond inhomogeneity for disordered polymorphs.

Pauli crystal melting in shaken optical traps

Pauli crystals are ordered geometric structures that emerge in trapped noninteracting fermionic systems due to their underlying Pauli repulsion. The deformation of Pauli crystals - often called melting - has been recently observed in experiments, but the mechanism that leads to it remains unclear. We address this question by studying the melting dynamics of N=6N=6 fermions as a function of periodic driving and experimental imperfections in the trap (anisotropy and anharmonicity) by employing a combination of numerical simulations and Floquet theory. Surprisingly, we reveal that the melting of Pauli crystals is not simply a direct consequence of an increase in system energy, but is instead related to the trap geometry and the population of the Floquet modes. We show that the melting is absent in traps without imperfections and triggered only by a sufficiently large shaking amplitude in traps with imperfections.

Topological defects of dipolar bose-einstein condensates with dresselhaus spin-orbit coupling in an anharmonic trap

We consider the topological defects and spin structures of binary Bose-Einstein condensates (BECs) with Dresselhaus spin-orbit coupling (D-SOC) and dipole-dipole interaction (DDI) in an anharmonic trap. The combined effects of D-SOC, DDI and anharmonic trap on the ground-state phases of the system are analyzed. Our results show various structural phase transitions can be achieved by adjusting the magnitudes of the D-SOC and DDI. Meantime, a ground-state phase diagram is given as a function of the D-SOC and DDI strengths. In addition, we find that tuning the D-SOC and the DDI can derive novel rich topological configurations, including ghost vortex, half-quantum vortex, skyrmion pair, vertical skyrmion string and horizontal skyrmion string.

Improved anharmonic trap expansion through enhanced shortcuts to adiabaticity

Shortcuts to adiabaticity (STA) have been successfully applied both theoretically and experimentally to a wide variety of quantum control tasks. In previous work the authors have developed an analytic extension to STA, called enhanced shortcuts to adiabaticity (eSTA), that extends STA methods to systems where STA cannot be applied directly (2020 Phys. Rev. Res. 2 023360). Here we generalize this approach and construct an alternative eSTA method that takes advantage of higher order terms. We apply this eSTA method to the expansion of both a Gaussian trap and accordion lattice potential, demonstrating the improved fidelity and robustness of eSTA.

Quench dynamics of two interacting atoms in a one-dimensional anharmonic trap

A temporal response of two interacting particles to a quench of the coupling strength in one-dimensional harmonic and anharmonic traps is explored. The coupling strength is changed from repulsive to attractive interactions and vice versa. The time evolution of the fidelity, wave packet, one-body reduced density matrix and momentum distributions is analyzed in details. It was found that impacts of the pre- and postquench states interchange during the dynamics. In the case of the anharmonic trap additional contribution of the center-of-mass excited states comes into play and the whole evolution becomes significantly altered. Yet the impact of the pre- and postquench states in some cases still could be identified. The quench dynamics of the ground and excited states are considered.

Dynamics of Rotating Spin-Orbit-Coupled Spin-1 Bose-Einstein Condensates With In-Plane Gradient Magnetic Field in an Anharmonic Trap

We investigate the dynamics of rotating spin-orbit-coupled spin-1 Bose–Einstein condensates (BECs) in an in-plane gradient magnetic field, which is confined in an anharmonic trap. In the case of rotating spin-orbit-coupled spin-1 BECs with given parameters, the system evolves from initial disk-shaped condensates into drastic turbulent oscillations and ghost vortices on the surface of the component densities due to surface wave excitations and then into two final vortex necklaces along the azimuthal direction with an irregular density hole, in which the vortices differ by one quantum number in turn. For the case of rotating spin-orbit-coupled spin-1 BECs with in-plane gradient magnetic field, with the dynamic evolution, the system undergoes a transition from an initial central polar-core vortex to violent turbulent oscillations and then to a final vortex chain along the diagonal of BECs, with the remaining vortices symmetrically distributed on both sides in the individual component. In addition, the corresponding spin texture undergoes a transition from plane-wave phase to double half-antiskyrmion necklaces for the former case and a transition from a structure similar to a quadrupole magnetic field to a half-antiskyrmion chain with the rest of the half-antiskyrmions on both sides. During the dynamic evolution process, the angular momentum increases gradually and then approaches a convergent value.

One- and two-qubit gate infidelities due to motional errors in trapped ions and electrons

In this work, we derive analytic formulae that determine the effect of error mechanisms on one- and two-qubit gates in trapped ions and electrons. First, we analyze, and derive expressions for, the effect of driving field inhomogeneities on one-qubit gate fidelities. Second, we derive expressions for two-qubit gate errors, including static motional frequency shifts, trap anharmonicities, field inhomogeneities, heating, and motional dephasing. We show that, for small errors, each of our expressions for infidelity converges to its respective numerical simulation; this shows our formulae are sufficient for determining error budgets for high-fidelity gates, obviating numerical simulations in future projects. All of the derivations are general to any internal qubit state, and any mixed state of the ion crystal's motion that is diagonal in the Fock state basis. Our treatment of static motional frequency shifts, trap anharmonicities, heating, and motional dephasing apply to both laser-based and laser-free gates, while our treatment of field imhomogenieties applies to laser-free systems.

Few Excited State Energies and Chemical Potential Energy of 87Rb Condensate by Many-Body Approach

We consider experimental 87Rb condensate which is trapped by harmonic plus quartic trap [V(r) = ½mω2r2 + λr4]. Keeping similarity with experiments, the anharmonic parameter (λ) is considered as a controllable parameter. The excited state energies of stable Bose-Einstein condensate are strongly influenced by the presence of an anharmonic term, even when the interatomic interaction is repulsive. The necessary dependencies of excited state energies of the trapped condensate on λ are discussed in detail. In addition, the variation of chemical potential energy as a function of λ is also investigated to explore the role of interaction. The many-particle Schrödinger equation is solved by the potential harmonic expansion method, where all possible two-body correlations are considered by utilizing the correlated two-body basis function. Specifically, we present a clear physical explanation of excited state energies and chemical potential energy of the experimental repulsive condensate confined by the anharmonic trap.

Study of Zero Temperature Ground State Properties of the Repulsive Bose-Einstein Condensate in an Anharmonic Trap

The zero-temperature ground state properties of experimental 87Rb condensate are studied in a harmonic plus quartic trap [ V(r) = ½mω2r2 + λr4 ]. The anharmonic parameter (λ) is slowly tuned from harmonic to anharmonic. For each choice of λ, the many-particle Schrödinger equation is solved using the potential harmonic expansion method and determines the lowest effective many-body potential. We utilize the correlated two-body basis function, which keeps all possible two-body correlations. The use of van der Waals interaction gives realistic pictures. We calculate kinetic energy, trapping potential energy, interaction energy, and total ground state energy of the condensate in this confining potential, modelled experimentally. The motivation of the present study is to investigate the crucial dependency of the properties of an interacting quantum many-body system on λ. The average size of the condensate has also been calculated to observe how the stability of repulsive condensate depends on anharmonicity. In particular, our calculation presents a clear physical picture of the repulsive condensate in an anharmonic trap.

Soliton dynamics of a high-density Bose-Einstein condensate subject to a time varying anharmonic trap

In this paper we study the soliton dynamics of a high-density Bose-Einstein condensate (BEC) subject to a time-oscillating trap. The behavior of the BEC is described with a modified Gross-Pitaevskii equation (mGPE) which takes into account three-body losses, atomic feeding and quantum fluctuations (up to a novel high-density term). A variational approximation (VA) is used to study the behavior of a Gaussian pulse in a static double-well potential. Direct numerical solutions of the mGPE corroborate that the center of the pulse exhibits an oscillatory behavior (as the VA predicts), and show a novel phenomenon of fragmentation and regeneration (FR). It is shown that this FR process is destroyed if we consider a potential with a time-dependent quadratic term, but the FR survives if the time dependence is introduced in a cubic term. Comparison between the VA and the numerical solution revealed an excellent agreement when the oscillations of the pulse remain in one of the potential wells. The effects of the quantum fluctuating terms on the FR process are studied. Finally, variational results using a supergaussian trial function are obtained.

Quantum control via enhanced shortcuts to adiabaticity

Fast and robust quantum control protocols are often based on an idealised approximate description of the relevant quantum system. While this may provide a performance which is close to optimal, improvements can be made by incorporating elements of the full system representation. We propose a new technique for such scenarios, called enhanced shortcuts to adiabaticity (eSTA). The eSTA method works for previously intractable Hamiltonians by providing an analytical correction to existing STA protocols. This correction can be easily calculated and the resulting protocols are outside the class of STA schemes. We demonstrate the effectiveness of the method for three distinct cases: manipulation of an internal atomic state beyond the rotating wave approximation, transport of a neutral atom in an optical Gaussian trap and transport of two trapped ions in an anharmonic trap.

Measurement of gravitational acceleration by cold atom multimode interference in the anharmonic potential

We investigated the anharmonic effects on the dynamics and measurement accuracy of a multimode cold atomic interferometer driven by two Kapitza–Dirac pulses. The first Kapitza–Dirac pulse creates several spatially addressable modes from the ground state of an anharmonic trap and the external field. These modes evolve along different paths and coherently recombine under the anharmonic potential. The second Kapitza–Dirac pulse separates these mixed modes again. The anharmonic effect causes the asymmetry of the density distribution function of the cold atoms and it is observed at the measurement time. The expected sensitivity is calculated by the Fisher information and the Cramér–Rao lower bound. As the anharmonic effect is enhanced, the measurement accuracy of the current atomic interferometer is slightly reduced relative to the measurement accuracy Δg∕g≈10−9 in the case of a harmonic trap.

Relaxation of atomic temperature anisotropy in a one-dimensional optical lattice enhanced by dynamic control of the aspect ratio

We study the relaxation dynamics of temperature anisotropy between longitudinal and transverse motions of $^{87}\mathrm{Rb}$ atoms in a one-dimensional optical lattice. The temperature imbalance is established by Raman sideband cooling applied along the lattice axis. At low temperature, a large difference between the longitudinal and transverse vibration frequencies limits the relaxation. We transform the trap potential by phase modulating the lattice beam to reduce the anisotropy and thereby enhance cross-dimensional sympathetic cooling. An extension of classical theory, which incorporates the quantization of the atomic motion, explains the experimental results well. We also report that effects of trap anharmonicity and atomic vector polarizability on broadening of the Raman sideband cancel each other at a particular lattice depth, which greatly facilitates sideband cooling.