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Entropy

STA-Mediated Interferometry with a Single Trapped Particle

Alvaro Rodriguez-Prieto, S. Martínez-Garaot, Ion Lizuain

Published Feb 28, 2026• 0 citations
Publisher

Abstract

We reviewand update schemes for different measurements using STA-mediated guided interferometry with a single trapped particle. STA stands for "shortcuts to adiabaticity", a set of techniques to achieve the results of adiabatic dynamics in shorter times. In the first scheme we presented a protocol aimed at detecting weak unknown forces. It consisted of a single ion trapped in a harmonic potential and driven by time-and-spin-dependent forces generated via off-resonant lasers. Our approach provided stability and the independence of the results on the motional states for the small-oscillations regime. We could, also, design faster-than-adiabatic processes with sensitivity control. However, it required a rotation of the trapping potential at the moment the experiment starts. A much more practical and broadly applicable design was then developed, where no rotation is involved. Here, a single atom is driven by two moving spin-dependent trapping potentials where we guide the arms of the interferometer via shortcuts to adiabatic paths. In this paper, in addition to a brief review of these two previous proposals, we revisit the first scheme and present a new protocol where the spin-dependent driving force is generated via a "shaken" optical lattice. This opens the possibility for additional interferometric measurements beyond an unknown force, for example, the mass of the trapped ion, while still preserving the advantages of the previously proposed method.

DOI
10.3390/e28030267

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•Jan 1, 2017•0 citations
We reviewand update schemes for different measurements using STA-mediated guided interferometry with a single trapped particle. STA stands for "shortcuts to adiabaticity", a set of techniques to achieve the results of adiabatic dynamics in shorter times. In the first scheme we presented a protocol aimed at detecting weak unknown forces. It consisted of a single ion trapped in a harmonic potential and driven by time-and-spin-dependent forces generated via off-resonant lasers. Our approach provided stability and the independence of the results on the motional states for the small-oscillations regime. We could, also, design faster-than-adiabatic processes with sensitivity control. However, it required a rotation of the trapping potential at the moment the experiment starts. A much more practical and broadly applicable design was then developed, where no rotation is involved. Here, a single atom is driven by two moving spin-dependent trapping potentials where we guide the arms of the interferometer via shortcuts to adiabatic paths. In this paper, in addition to a brief review of these two previous proposals, we revisit the first scheme and present a new protocol where the spin-dependent driving force is generated via a "shaken" optical lattice. This opens the possibility for additional interferometric measurements beyond an unknown force, for example, the mass of the trapped ion, while still preserving the advantages of the previously proposed method.
We propose an interferometric measurement of weak forces using a single ion subjected to designed time-dependent spin-dependent forces. Explicit expressions of the relation between the unknown force and the final populations are found considering different scenarios, such as the weak force acting on two branches, acting on one branch, or having errors in the driving force. The flexibility to design the trap trajectories is used to minimize errors due to anharmonicities in the trap. The advantages of the approach are the use of geometrical phases, which provides stability, the possibility to design faster-than-adiabatic processes with sensitivity control, and the independence of the results on the motional states for the small-oscillations regime in which the effective potentials are purely harmonic.
We propose a compact atom interferometer to measure homogeneous constant forces guiding the arms via shortcuts to adiabatic paths.For a given sensitivity, which only depends on the space-time area of the guiding paths, the cycle time can be made fast without losing visibility.The atom is driven by spin-dependent trapping potentials moving in opposite directions, complemented by linear and time-dependent potentials that compensate the trap acceleration.Thus, the arm states are adiabatic in the moving frames and nonadiabatic in the laboratory frame.The trapping potentials may be anharmonic, e.g., optical lattices, and the interferometric phase does not depend on the initial motional state or on the pivot point for swaying the linear potentials.
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.
Fast and robust quantum control protocols are often based on an idealized approximate description of the relevant quantum system.While this may provide a performance that is close to optimal, improvements can be made by incorporating elements of the full system representation.We propose a 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.
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.
Adiabatic processes in quantum mechanics are very useful to prepare and manipulate quantum states but have the drawback of requiring long operation times. Hence there is a long time for the system to interact with its environment which can lead to a loss of coherence of the final state. This decoherence is problematic for implementing future quantum technologies which require the state's quantum mechanical features. “Shortcuts to Adiabaticity"(STA) provides a toolbox of methods to improve on adiabatic processes. Using these methods one can derive alternative processes which work for much shorter times with perfect fidelity. Since adiabatic processes are ubiquitous in atomic, molecular and optical physics, there is a broad scope of application for STA. In this thesis, STA (especially those using Lewis-Riesenfeld invariants) are applied to a variety of quantum systems for the purpose of quantum state transfer. In particular I show that STA control schemes in two- and three-level systems can be optimised to be more stable against unwanted uncontrollable transitions than adiabatic methods with the same operation time. I also show that STA methods can be applied in a triple well ring system with complex tunnelling, in optical lattices for the purposes of generating a higher orbital state of neutral atoms and in Penning traps to quickly compress or expand the trapped ion wavefunction. Finally I also investigate the effect of classical Poisson white noise on adiabatic processes.