It is shown that in an anisotropic harmonic trap that rotates with the properly chosen rotation rate, the force of gravity leads to a resonant behavior. Full analysis of the dynamics in an anisotropic, rotating trap in 3D is presented and several regions of stability are identified. On resonance, the oscillation amplitude of a single particle, or of the center of mass of a many-particle system (for example, BEC), grows linearly with time and all particles are expelled from the trap. The resonances can only occur when the rotation axis is tilted away from the vertical position. The positions of the resonances (there are always two of them) do not depend on the mass but only on the characteristic frequencies of the trap and on the direction of the angular velocity of rotation.
We engineer the fast rotation of a quantum particle confined in an effectively one-dimensional, harmonic trap, for a predetermined rotation angle and time, avoiding final excitation. Different schemes are proposed with different speed limits that depend on the control capabilities. We also make use of trap rotations to create squeezed states without manipulating the trap frequencies.
We report sensitive detection of parametric resonances in a high-density sample of ultracold $^{87}Rb$ atoms confined to a far-off-resonance optical dipole trap. Fluorescence imaging of the expanded ultracold atom cloud after a period of parametric excitation shows significant modification of the atomic spatial distribution and has high sensitivity compared with traditional measurements of parametrically-driven trap loss. Using this approach, a significant shift of the parametric resonance frequency is observed, and attributed to the anharmonic shape of the dipole trap potential.
We investigate the impact of a rotating wall potential on perpendicular laser cooling in a Penning ion trap. By including energy exchange with the rotating wall, we extend previous Doppler laser cooling theory and show that low perpendicular temperatures are more readily achieved with a rotating wall than without. Detailed numerical studies determine optimal operating parameters for producing low temperature, stable 2-dimensional crystals, important for quantum information processing experiments employing Penning traps.
Trapped ions boast long coherence times and excellent gate fidelities, making them a useful platform for quantum information processing. Scaling to larger numbers of ion qubits in RF Paul traps demands great effort. Another technique for trapping ions is via a Penning trap where a 2D crystal of hundreds of ions is formed by controlling the rotation of the ions in the presence of a strong magnetic field. However, the rotation of the ion crystal makes single ion addressability a significant challenge. We propose a protocol that takes advantage of a deformable mirror to introduce AC Stark shift p…
Programmable coherent site-selective spin control in rotating Penning-trap ion crystals
School of Physics, The University of Sydney（悉尼大学物理学院）；Department of Physics, Indian Institute of Technology Madras（马德拉斯理工学院物理系）；Center for Quantum Information, Communication and Computing, Indian Institute of Technology Madras（马德拉斯理工学院量子信息、通信与计算中心）；Sydney Nano Institute, The University of Sydney（悉尼大学悉尼纳米研究所）
The dynamics of two-component Bose-Einstein condensates in rotating traps is investigated. In the Thomas-Fermi limit, equations of motion are derived showing multiple static solutions for a vortex free condensate. Dynamic stability analysis of these solutions and comparison with Truncated Wigner simulations enables us to identify the regimes for which vortex states will occur. In addition, our analysis predicts centre-of-mass oscillations that are induced by interspecies interactions and affect each component separately. For attractive interspecies interactions, these oscillations lead to a st…
One of the challenges with quantum simulation in ion traps is that the effective spin-spin exchange couplings are not uniform across the lattice. This can be particularly important in Penning trap realizations where the presence of an ellipsoidal boundary at the edge of the trap leads to dislocations in the crystal. By adding an additional anharmonic potential to better control interion spacing, and a triangular shaped rotating wall potential to reduce the appearance of dislocations, one can achieve better uniformity of the ionic positions. In this work, we calculate the axial phonon frequenci…
Fractional quantum Hall systems are among the most exciting strongly correlated systems. Accessing them microscopically via quantum simulations with ultracold atoms would be an important achievement toward a better understanding of this strongly correlated state of matter. A promising approach is to confine a small number of bosonic atoms in a quasi-two-dimensional rotating trap, which mimics the magnetic field. For rotation frequencies close to the in-plane trapping frequency, the ground state is predicted to be a bosonic analog of the Laughlin state. Here, we study the problem of the adiabat…
Exact two-dimensional analytic wave functions for an arbitrary number $N$ of contact-interacting lowest-Landau-level (LLL) spinful fermions are derived with the use of combined numerical and symbolic computational approaches via analysis of exact Hamiltonian numerical diagonalization data. Closed-form analytic expressions are presented for two families of zero-interaction-energy states at given total angular momentum and total spin $0 \leq S \leq N/2$ in the neighborhood of the $ν=1$ filling, covering the range from the maximum density droplet to the first quasihole. Our theoretical prediction…
We describe a new mechanism of tunneling between period-two vibrational states of a weakly nonlinear parametrically modulated oscillator. The tunneling results from resonant transitions induced by the fast oscillating terms conventionally disregarded in the rotating wave approximation (RWA). The tunneling amplitude displays resonant peaks as a function of the modulation frequency; near the maxima it is exponentially larger than the RWA tunneling amplitude.
Phases of a rotating Bose-Einstein condensate trapped in a hard-wall potential
Université Sorbonne Paris Nord（巴黎索邦大学）；CNRS（法国国家科学研究中心）；Hellenic Mediterranean University（希腊地中海大学）；HMU Research Center, Institute of Emerging Technologies（HMU新兴技术研究所）
We report observations of the Electron Spin Resonance (ESR) of Nitrogen Vacancy (NV) centers in diamonds that are levitating in an ion trap. Using a needle Paul trap operating under ambient conditions, we demonstrate efficient microwave driving of the electronic spin and show that the spin properties of deposited diamond particles measured by the ESR are retained in the Paul trap. We also exploit the ESR signal to monitor the rotation of levitating monocrystals, a first step towards spin-controlled mechanical systems in scattering-free traps.
Employing a short-range two-channel description we derive an analytic model of atoms in isotropic and anisotropic harmonic traps at a Feshbach resonance. On this basis we obtain a new parameterization of the energy-dependent scattering length which differs from the one previously employed. We validate the model by comparison to full numerical calculations for Li-Rb and explain quantitatively the experimental observation of a resonance shift and trap-induced molecules in exited bands. Finally, we analyze the bound state admixture and Landau-Zener transition probabilities.
We present a study on the trapping of hard ferromagnetic particles using alternating magnetic fields, with a focus on planar trap geometries. First, we realize and characterize a magnetic Paul trap design for millimeter-size magnets based on a rotating magnetic potential. Employing a physically rotating platform with two pairs of permanent magnets with opposite poles, we show stable trapping of hard ferromagnets a centimeter above the trap and demonstrate that the particle shape plays a critical role in the trapping. Finally, we propose a chip trap design that will open a path to studies of gy…
Feshbach resonances are among the essential control tools used in ultracold atom experiments. However, for complex atomic species the theoretical characterization of resonances becomes challenging. For closely spaced resonances, the measurement of three-body losses does not provide sufficient resolution to discriminate them. For this reason, resonance spectroscopy of trapped isolated atoms is becoming the state of the art. Here we show that trapping the atoms in a double well potential such as an optical lattice or a pair of optical tweezers enables precise characterization of not only the res…
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.
Overlapping Feshbach resonances are commonly observed in experiments with ultracold atoms and can influence the molecule production process. We derive an effective approach to describe magnetoassociation in an external trap in the presence of multiple overlapping resonances. We study how the strength and shape of the trap affects the energy level structure and demonstrate the existence of a regime in which the conventional two-channel Landau-Zener description of the molecule production process breaks down.
The fractional quantum Hall effect (FQHE) is theoretically investigated, with numerical and algebraic approaches, in assemblies of a few spinful ultracold neutral fermionic atoms, interacting via repulsive contact potentials and confined in a single rapidly rotating two-dimensional harmonic trap. Going beyond the commonly used second-order correlations in the real configuration space, the methodology in this paper will assist the analysis of experimental observations by providing benchmark results for $N$-body spin-unresolved, as well as spin-resolved, momentum correlations measurable in time-…
