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arXiv:1902.03354 · New Journal of Physics

Bang-bang shortcut to adiabaticity in the Dicke model as realized in a Penning trap experiment

Jeffrey Cohn, Arghavan Safavi-Naini, Robert J. Lewis-Swan, Justin Bohnet, Martin Gärttner, Kevin Gilmore, J E Jordan, Ana María Rey, J. J. Bollinger, James K. Freericks

Published May 11, 2018• 45 citations
arXivHTMLPDF

Abstract

We introduce a bang-bang shortcut to adiabaticity for the Dicke model, which we implement via a two-dimensional array of trapped ions in a Penning trap with a spin-dependent force detuned close to the center-of-mass drumhead mode. Our focus is on employing this shortcut to create highly entangled states that can be used in high-precision metrology. We highlight that the performance of the bang-bang approach is comparable to standard preparation methods, but can be applied over a much shorter time frame. We compare these theoretical ideas with experimental data which serve as a first step towards realizing this theoretical procedure for generating multi-partite entanglement.

DOI
10.1088/1367-2630/aac3fa

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We introduce a bang-bang shortcut to adiabaticity for the Dicke model, which we implement via a two-dimensional array of trapped ions in a Penning trap with a spin-dependent force detuned close to the center-of-mass drumhead mode. Our focus is on employing this shortcut to create highly entangled states that can be used in high-precision metrology. We highlight that the performance of the bang-bang approach is comparable to standard preparation methods, but can be applied over a much shorter time frame. We compare these theoretical ideas with experimental data which serve as a first step towards realizing this theoretical procedure for generating multi-partite entanglement.
We model the bang-bang optimization protocol as a shortcut to adiabaticity in the ground-state preparation of a trapped-ion quantum simulator. Compared to a locally adiabatic evolution, the bang-bang protocol typically produces a lower ground-state probability, but its implementation is so much simpler than the locally adiabatic approach, that it can become a competitive choice to use for maximizing ground-state preparation in systems that cannot be solved with conventional computers. We describe how one can optimize the shortcut and provide specific details for how it can be implemented with current trapped-ion quantum simulators. However, when frustration is strong enough, no method appears to work well for adiabatic state preparation within the experimental time frames, and one must confront the issue of dealing with diabatic excitations within the simulation.
We use a self-assembled two-dimensional Coulomb crystal of ∼70\sim 70∼70 ions in the presence of an external transverse field to engineer a quantum simulator of the Dicke Hamiltonian. This Hamiltonian has spin and bosonic degrees of freedom which are encoded by two hyperfine states in each ion and the center of mass motional mode of the crystal, respectively. The Dicke model features a quantum critical point separating two distinct phases: the superradiant (ferromagnetic) and normal (paramagnetic) phases. We experimentally explore protocols that aim to adiabatically prepare the superradiant ground state, a spin-boson cat state with macroscopic phonon occupation, which is well-suited for enhanced metrology and quantum information processing. We start in the normal phase, with all spins aligned along a large transverse field and ramp down the field across the critical point following various protocols. We measure the spin observables, both experimentally and in our simulations to characterize the state of the system at the end of the ramp. We find that under current operating conditions an optimally designed ramp is not sufficient to achieve significant fidelity with the superradiant ground state. However, our theoretical investigation shows that slight modifications of experimental parameters, together with modest reductions in decoherence rates and thermal noise can increase the cat-state fidelity to ∼75%\sim 75\%∼75% for N∼20N \sim 20N∼20 spins. Our results open a path for the use of large ensembles of trapped ions as powerful quantum sensors and quantum computers.
In this dissertation we focused on some quantum states with strong entanglement and robustness to noise. We constructed a spinor BEC Hamiltonian which has already been realized in experiment with several different kinds of atoms and proposed an adiabatic passage method to produce the maximal entangled Dicke state. We also analyzed the entanglement behavior of the Dicke state under various noises and demonstrate its use in high precision measurement experiment. We introduce a new class of quantum many-particle entangled states, called the Dicke squeezed (or DS) states, which can be used to improve the precision in quantum metrology beyond the standard quantum limit. We show that the enhancement in measurement precision is characterized by a single experimentally detectable parameter, called the Dicke squeezing, which also bounds the entanglement depth for this class of states. The measurement precision approaches the ultimate Heisenberg limit as the Dicke squeezing parameter attains the minimum in an ideal Dicke state. Compared with other entangled states, we show that the Dicke squeezed states are more robust to decoherence and give better measurement precision under typical experimental noise. On the other hand, we explore other choices of precision measurement with spin squeezed states. Spin squeezed states have strong manybody entanglement and are good candidates to be used in quantum metrology. A robust squeezing parameter is proposed to characterize the experimental phase measurement precision for spin squeezed states. The behavior of this parameter under various experimental noises is compared with other parameters in the history and it is shown to have better performance. Finally we present a scalable implementation scheme for Boson sampling using local transverse phonon modes in trapped ion system, which is a promising model for quantum computers.
Exact simulation of quantum systems is intractable on current classical computers due to the time required to calculate the exponential number of amplitudes which represent a quantum state.This thesis explores how highly tuned quantum devices, such as quantum simulators and digital quantum computers, can be utilized to gain a deeper understanding of nature.In Chapter 1 we begin by reviewing some of the basics of quantum information.Chapter 2 highlights the advantages of using entangled states in metrology and how quantum simulators can be realized on a system of trapped ions.Chapter 3 develops the gate model of quantum computing and reviews many of the foundational algorithms needed to simulate many-body systems.Chapter 4 originates from the paper "Verification of a many-ion simulator of the Dicke model through slow quenches across a phase transition."[1].This chapter examines how a system of trapped ions can be engineered to emulate a famous model known as the Dicke model, which involves coupling many spins to a single bosonic mode.After confirming that the Dicke model indeed has been realized, we show in Chapter 5 how simple protocols can be used to prepare highly entangled states.This chapter originates from the paper, "Bang-bang shortcut to adiabaticity in the Dicke model as realized in a Penning trap experiment" [2].These states have the potential to provide giant gains in making precision measurements.Finally, with the use of universal quantum computers on the horizon, we develop a framework, in Chapter 6, for extracting thermal properties of many-body systems on these machines.This chapter eminates Many thanks are in order for the people who helped me get to where I am in my career.First, my parents, Robert and Maureen Cohn, who have always been there to support me.In this respect I am also grateful for the support provided by my grandparents Alien and Joeseph
Dicke state is one of the most useful multipartite quantum states. In this paper, by utilizing the method of designing the evolution operators to construct shortcuts to adiabatic passages (STAP), we have implemented the fast preparation of Dicke states |D3(2)〉 and |D4(2)〉 with one step. Specifically, with the assistance of quantum Zeno dynamics, the original Hamiltonian of the system is simplified into an effective Hamiltonian. Under the dynamic evolution of this effective Hamiltonian, the pulse control is realized by selecting two appropriate auxiliary parameters. This not only greatly shortens the evolution time but also optimizes the operation of the quantum system. In addition, we have discussed the effects of decoherence, parameter fluctuations and noise on fidelity. The results indicate that the proposed protocol maintains high fidelity. Finally, the fast preparation of Dicke state |Dn(2)〉 can be achieved based on the same method.
We use a self-assembled two-dimensional Coulomb crystal of ∼70 ions in the presence of an external transverse field to engineer a simulator of the Dicke Hamiltonian, an iconic model in quantum optics which features a quantum phase transition between a superradiant (ferromagnetic) and a normal (paramagnetic) phase. We experimentally implement slow quenches across the quantum critical point and benchmark the dynamics and the performance of the simulator through extensive theory-experiment comparisons which show excellent agreement. The implementation of the Dicke model in fully controllable trapped ion arrays can open a path for the generation of highly entangled states useful for enhanced metrology and the observation of scrambling and quantum chaos in a many-body system.