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arXiv:2306.09238 · Physical Review A

Excited-state preparation of trapped ultracold atoms via swept potentials

Daniel J. Bosworth, Maxim Pyzh, Peter Schmelcher

Published Jan 12, 2024• 1 citation
arXivHTMLPDF

Abstract

We study the out-of-equilibrium dynamics of noninteracting atoms confined within a one-dimensional harmonic trap triggered by dragging an external long-range potential through the system. The symmetry-breaking nature of this moving potential couples adjacent eigenstates in the atoms' effective potential, leading to an energy landscape reminiscent of systems exhibiting trap-induced shape resonances. These couplings may be exploited to selectively excite the atoms into higher vibrational states of the harmonic trap by controlling the motion of the dragged potential. To this end, we consider two protocols designs: The first protocol strives to maintain adiabaticity at critical points during the atoms' dynamics, while the second protocol utilizes the fast tunneling of the atoms within their effective double-well potential. These protocols take place in the few to many millisecond regime and achieve high-fidelity excitation of the atoms into pure vibrational states and superpositions thereof. Overall, our study highlights the significance of dragged potentials for controlling and manipulating atom dynamics and offers intuitive protocols for achieving desired excitations.

DOI
10.1103/physreva.109.013311

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We study the out-of-equilibrium dynamics of noninteracting atoms confined within a one-dimensional harmonic trap triggered by dragging an external long-range potential through the system. The symmetry-breaking nature of this moving potential couples adjacent eigenstates in the atoms' effective potential, leading to an energy landscape reminiscent of systems exhibiting trap-induced shape resonances. These couplings may be exploited to selectively excite the atoms into higher vibrational states of the harmonic trap by controlling the motion of the dragged potential. To this end, we consider two protocols designs: The first protocol strives to maintain adiabaticity at critical points during the atoms' dynamics, while the second protocol utilizes the fast tunneling of the atoms within their effective double-well potential. These protocols take place in the few to many millisecond regime and achieve high-fidelity excitation of the atoms into pure vibrational states and superpositions thereof. Overall, our study highlights the significance of dragged potentials for controlling and manipulating atom dynamics and offers intuitive protocols for achieving desired excitations.
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Highly excited eigenstates of the motion of an individual spatially confined atom may be prepared making use of a “trapping” mechanism based on the nonlinearity of the laser-mediated coupling of internal excitation and center-of-mass vibration of the atom. In contrast to micromaser-type trapping states, these states are insensitive to laser-phase fluctuations, and a long sequence of laser pulses may be applied to the atom with little degradation only of the atomic motion. Thus, vibrational number states of high quantum numbers are achievable.
Time-varying fields are widely used to extend the accessible range of trapping potentials for ultracold atoms. This work explores two very different examples of such fields, in the radiofrequency and optical regimes, whose interactions with trapped atoms can both be described in terms of the dressed atom picture. Forming the basis of this work are radiofrequency dressed adiabatic potentials based on macroscopic trapping coils. Atoms are confined at the south pole of the resultant oblate spheroidal trapping surfaces. This work describes the extension of these potentials by two different methods: the application of multiple dressing radiofrequencies, and addition of a rapidly-scanned optical dipole trap. This is the first experimental demonstration of a multiple-radiofrequency dressed adiabatic potential, explored using ultracold 87Rb atoms confined in a highly configurable double well. Due to the independent generation of each constituent dressing frequency, the depth of each trapping well and the height of the barrier are easily manipulated, enabling precise and reliable transfer of atoms between the available trapping geometries. Experimental work includes an exploration of the potential-shaping capabilities of the three-radiofrequency system, and characterisation of the potential landscape using radiofrequency spectroscopy with good agreement to the eigenvalues numerically calculated using Floquet theory. This initial exploration of multiple-radiofrequency techniques lays the groundwork for applications in studying double well physics in a two-dimensional system, and independent state or species selective manipulation of trapped atoms. The potential shaping capabilities of this method can also be extended by applying additional trapping frequencies. In a supplementary line of experimental work, an optical dipole trapping system has been constructed, and the trapping beam aligned to the lower surface of the radiofrequency dressed trapping shell in order to sculpt the radial confinement. Beam shaping is achieved using an acousto-optic deflector, which can be used to produce either a composite array of static deflected beams, a rapidly-scanned painted potential, or some combination of the two approaches. The development and extension of the experimental apparatus required to implement these enhanced dressed state potentials is explored, and the challenges of their experimental implementation considered.
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We consider controlled collisions between two ultracold atoms guided by external harmonic potentials. We derive analytical solutions of the Schr\"odinger equation for this system and investigate the properties of eigenergies and eigenstates for different trap geometries as a function of a trap separation and of the scattering length. When varying the trap separation the energy spectrum exhibits avoided crossings, corresponding to trap-induced shape resonances. Introducing an energy-dependent scattering length we investigate the behavior of the system in the vicinity of a magnetic Feshbach resonance. Finally, we illustrate our analytical results with two examples: the quantum phase gate controlled by the external magnetic field and a scheme for a coherent transport of atoms in optical lattices into higher Bloch bands.
Precise control of quantum particles is required for many interesting or novel experiments. Here we consider the task of transporting an atom using an external harmonic potential from one well of an optical lattice to another without motional excitations. To achieve this we apply techniques from Shortcuts to Adiabaticity (STA) enabling fast and robust state manipulation. The process is split up into three independent building blocks; first the atom is loaded into an additional external harmonic trap; this trap is then transported from one lattice site to another and finally the atom is unloaded back onto the lattice by opening the external harmonic trap. We design protocols for each of these building blocks separately using invariant-based inverse engineering. Additionally we extend this method to the transport of a Bose-Einstein condensate described by the Gross-Pitaevskii equation.