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arXiv:1912.06057 · Physical Review Research

Quantum control via enhanced shortcuts to adiabaticity

C. Whitty, A. Kiely, A. Ruschhaupt

Published Jun 18, 2020• 37 citations
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Abstract

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.

DOI
10.1103/physrevresearch.2.023360

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•Jun 19, 2020•0 citations
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.
Shortcuts to adiabaticity (STA) are a collection of quantum control techniques that achieve high fidelity outside of the adiabatic regime. Recently an extension to shortcuts to adiabaticity was proposed by the authors [Whitty, Kiely, and Ruschhaupt, Phys. Rev. Research 2, 023360 (2020)]. This method, enhanced shortcuts to adiabaticity (eSTA), provides an extension to the original STA control functions and allows effective control of systems not amenable to STA methods. It is conjectured that eSTA schemes also enjoy an improved stability over their STA counterparts. We provide numerical evidence of this claim by applying eSTA to fast atomic transport using an optical lattice and evaluating appropriate stability measures. We show that the eSTA schemes not only produce higher fidelities but also remain more stable against errors than the original STA schemes.
Abstract 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.
The technique of shortcuts to adiabaticity (STA) has attracted broad attention due to their possible applications in quantum information processing and quantum control. However, most studies published so far have been only focused on Hermitian systems under the rotating-wave approximation (RWA). In this paper, we propose a modified shortcuts to adiabaticity technique to realize population transfer for a non-Hermitian system without RWA. We work out an exact expression for the control function and present examples consisting of two-and three-level systems with decay to show the theory. The results suggest that the shortcuts to adiabaticity technique presented here is robust for fast passages. We also find that the decay has small effect on the population transfer in the three-level system. To shed more light on the physics behind this result, we reduce the quantum three-level system to an effective two-level one with large detunings. The shortcuts to adiabaticity technique of effective two-level system is studied. Thereby the high-fidelity population transfer can be implemented in non-Hermitian systems by our method, and it works even without RWA.
Achieving fast, excitation-free quantum control is a vital challenge in modern quantum technologies. In many cases, shortcuts to adiabaticity enable fast adiabatic-like protocols, yet determining control parameters that satisfy practical constraints is often challenging in complex systems. Here, we combine an analytical shortcut to adiabaticity approach with several numerical optimization methods to boost the performance of the protocol. As a proof-of-principle for this hybrid approach, we study a particularly intricate control problem, the separation of two trapped ions. We show that this analytical-numerical approach, along with the physical insight gained through the variety of suboptimal solutions, leads to the exploration of new solutions in a complex landscape that yield improvements of up to 3 orders of magnitude. Moreover, this improvement comes with no additional cost from an experimental point of view.
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.
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.