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arXiv:2002.05976

Transport of atoms across an optical lattice using an external harmonic potential

Tom Dowdall, A. Ruschhaupt

Published Feb 14, 2020• 1 citation
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Abstract

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.

DOI
10.48550/arxiv.2002.05976

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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.
Fast and nearly lossless atomic transport, enabled by moving the confining trap, is a prerequisite for many quantum-technology applications. While theoretical studies of this problem have heretofore focused almost exclusively on simplified scenarios (one-dimensional systems, purely harmonic confining potentials, etc.), we investigate it here in the experimentally relevant setting of a moving optical lattice (optical conveyor belt). We model single-atom transport in this system by taking fully into account its three-dimensional, anharmonic confining potential. We do so using the established method of shortcuts to adiabaticity (STA), i.e., an inverse-engineering approach based on Lewis-Riesenfeld invariants, as well as its recently proposed modification known as enhanced STA (eSTA). By combining well-controlled, advanced analytical techniques and the numerical propagation of a time-dependent Schr\"odinger equation using the Fourier split operator method, we evaluate atom-transport fidelities within both approaches. Being obtained for realistic choices of system parameters, our results are relevant for future experiments with optical conveyor belts. Moreover, they reveal that in the system at hand the eSTA method outperforms its STA counterpart for all but the lowest optical-lattice depths.
We study the fast transport of a particle or a Bose-Einstein condensate in a harmonic potential. An exact expression for the final excitation energy in terms of the Fourier transform of the trap acceleration is used to engineer optimal transport protocols (with no final excitation) that are robust with respect to spring-constant errors. The same technique provides a way to design the simultaneous and robust transport of a few noninteracting species that experience different harmonic trap frequencies in the same trap.
A major barrier for the development of new quantum technologies is fast and robust methods for preparing and manipulating complex quantum states. To date preparation and manipulation of quantum systems has primarily been done using adiabatic processes. These adiabatic processes while robust have significant disadvantages such as their requiring long process times, a further drawback is that the system-environment interaction over these these long process times can lead to loss of coherence of the state of the system. A new area of study to achieve the robustness of adiabatic schemes but in time-scales much shorter is "Shortcuts to Adiabaticity" (STA). These STA techniques provide new methods for the manipulation of quantum systems that achieve high-fidelity state transfers in much shorter times. The aim of this thesis is to use STA and related methods for many particle systems. A method for manipulating a gas of fermions is developed using Pauli blocking and it’s robustness in the presence of temperature and different particle number investigated. A novel method for trapping and cooling particles using atom-diode and reflecting atomic mirror is investigated, both the classical and quantum cases are simulated. A method for transporting atoms and condensates across an optical lattice using invariant based inverse engineering is developed. Finally we look at non-hermitian potentials and design particular potentials that result in desirable asymmetries in the transmission and reflection of incident particles.
We investigate fast transport and spin manipulation of tunable spin-orbit-coupled Bose-Einstein condensates in a moving harmonic trap. Motivated by the concept of shortcuts to adiabaticity, we design inversely the time-dependent trap position and spin-orbit-coupling strength. By choosing appropriate boundary conditions we obtain fast transport and spin flip simultaneously. The nonadiabatic transport and relevant spin dynamics are illustrated with numerical examples and compared with the adiabatic transport with constant spin-orbit-coupling strength and velocity. Moreover, the influence of nonlinearity induced by interatomic interaction is discussed in terms of the Gross-Pitaevskii approach, showing the robustness of the proposed protocols. With the state-of-the-art experiments, such an inverse engineering technique paves the way for coherent control of spin-orbit-coupled Bose-Einstein condensates in harmonic traps.
Theoretical studies of coherent atom transport have as yet mainly been restricted to one-dimensional model systems with harmonic trapping potentials. Here we investigate this important phenomenon---a prerequisite for a variety of quantum-technology applications based on cold neutral atoms---under much more complex physical circumstances. More specifically yet, we study fast atomic transport in a moving double-well optical lattice, whose three-dimensional (anharmonic) potential is nonseparable in the xxx-yyy plane. We first propose specific configurations of acousto-optic modulators that give rise to the moving-lattice effect in an arbitrary direction in this plane. We then determine moving-lattice trajectories that enable single-atom transport using two classes of quantum-control methods: shortcuts to adiabaticity (STA), here utilized in the form of inverse engineering based on a quadratic-in-momentum dynamical invariant of Lewis-Riesenfeld type, and their recently proposed modification termed enhanced STA (eSTA). Subsequently, we quantify the resulting single-atom dynamics by numerically solving the relevant time-dependent Schr\"odinger equations and compare the efficiency of STA- and eSTA-based transport by evaluating the respective fidelities. We show that---except for the regime of shallow lattices---the eSTA method consistently outperforms its STA counterpart. This study has direct implications for neutral-atom quantum computing based on collisional entangling two-qubit gates and quantum sensing of constant homogeneous forces via guided-atom interferometry.
We present an effective and fast (few microseconds) procedure for transferring a Bose–Einstein condensate from the ground state in a harmonic trap into the desired bands of an optical lattice. Our shortcut method is a designed pulse sequence where the time duration and the interval in each step are fully optimized in order to maximize robustness and fidelity of the final state with respect to the target state. The atoms can be prepared in a single band with even or odd parity, and superposition states of different bands can be prepared and manipulated. Furthermore, we extend this idea to the case of two-dimensional or three-dimensional optical lattices where the energies of excited states are degenerate. We experimentally demonstrate various examples and show very good agreement with the theoretical model. Efficient shortcut methods will find applications in the preparation of quantum systems, in quantum information processing, in precise measurement and as a starting point to investigate dynamics in excited bands.