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arXiv:1301.3646 · Physical Review A

Quantum quenches of ion Coulomb crystals across structural instabilities. II. Thermal effects

Jens D. Baltrusch, Cecilia Cormick, Giovanna Morigi

Published Mar 27, 2013• 4 citations
arXivHTMLPDF

Abstract

We theoretically analyze the efficiency of a protocol for creating mesoscopic superpositions of ion chains, described in Baltrusch et al. [Phys. Rev. A 84, 063821 (2011)], as a function of the temperature of the crystal. The protocol makes use of state-dependent forces, so that a coherent superposition of the electronic states of one ion evolves into an entangled state between the chain's internal and external degrees of freedom. Ion Coulomb crystals are well isolated from the external environment and should therefore experience a coherent, unitary evolution, which follows the quench and generates structural Schr\"odinger-cat-like states. The temperature of the chain, however, introduces a statistical uncertainty in the final state. We characterize the quantum state of the crystal by means of the visibility of Ramsey interferometry performed on one ion of the chain and determine its decay as a function of the crystal's initial temperature. This analysis allows one to determine the conditions on the chain's initial state in order to efficiently perform the protocol.

DOI
10.1103/physreva.87.032116

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We theoretically analyze the efficiency of a protocol for creating mesoscopic superpositions of ion chains, described in Baltrusch et al. [Phys. Rev. A 84, 063821 (2011)], as a function of the temperature of the crystal. The protocol makes use of state-dependent forces, so that a coherent superposition of the electronic states of one ion evolves into an entangled state between the chain's internal and external degrees of freedom. Ion Coulomb crystals are well isolated from the external environment and should therefore experience a coherent, unitary evolution, which follows the quench and generates structural Schr"odinger-cat-like states. The temperature of the chain, however, introduces a statistical uncertainty in the final state. We characterize the quantum state of the crystal by means of the visibility of Ramsey interferometry performed on one ion of the chain and determine its decay as a function of the crystal's initial temperature. This analysis allows one to determine the conditions on the chain's initial state in order to efficiently perform the protocol.
Quenches in an ion chain can create coherent superpositions of motional states across the linear-zigzag structural transition. The procedure has been described in Baltrusch et al. [Phys. Rev. A 84, 063821 (2011)] and makes use of spin-dependent forces, so that a coherent superposition of the electronic states of one ion evolves into an entangled state between the chain's internal and external degrees of freedom. The properties of the crystalline state so generated are theoretically studied by means of Ramsey interferometry on one ion of the chain. An analytical expression for the visibility of the interferometric measurement is obtained for a chain of an arbitrary number of ions and as a function of the time elapsed after the quench. Sufficiently close to the linear-zigzag instability the visibility decays very fast, but exhibits revivals at the period of oscillation of the mode that drives the structural instability. These revivals have a periodicity that is independent of the crystal size, and they signal the creation of entanglement by the quantum quench.
A procedure is discussed for creating coherent superpositions of motional states of ion strings. The motional states are across the structural transition linear-zigzag, and their coherent superposition is achieved by means of spin-dependent forces, such that a coherent superposition of the electronic states of one ion evolves into an entangled state between the chain's internal and external degrees of freedom. It is shown that the creation of such an entangled state can be revealed by performing Ramsey interferometry with one ion of the chain.
Coulomb crystals of cold trapped ions are a leading platform for the realization of quantum processors and quantum simulations and, in quantum metrology, for the construction of optical atomic clocks and for fundamental tests of the standard model. For these applications, it is not only essential to cool the ion crystal in all its degrees of freedom down to the quantum ground state but also to be able to determine its temperature with a high accuracy. However, when a large ground-state cooled crystal is interrogated for thermometry, complex many-body interactions take place, making it challenging to accurately estimate the temperature with established techniques. In this work, we present a new thermometry method tailored for ion crystals. The method is applicable to all normal modes of motion and does not suffer from a computational bottleneck when applied to large ion crystals. We test the temperature estimate with two experiments, namely with a one-dimensional linear chain of four ions and a two-dimensional crystal of 19 ions and verify the results, where possible, using other methods. The results show that the new method is an accurate and efficient tool for thermometry of ion crystals.
Coulomb crystals of cold trapped ions are a leading platform for the realization of quantum processors and quantum simulations and, in quantum metrology, for the construction of optical atomic clocks and for fundamental tests of the standard model.For these applications, it is not only essential to cool the ion crystal in all its degrees of freedom down to the quantum ground state but also to be able to determine its temperature with a high accuracy.However, when a large ground-state cooled crystal is interrogated for thermometry, complex many-body interactions take place, making it challenging to accurately estimate the temperature with established techniques.In this work, we present a new thermometry method tailored for ion crystals.The method is applicable to all normal modes of motion and does not suffer from a computational bottleneck when applied to large ion crystals.We test the temperature estimate with two experiments, namely with a one-dimensional linear chain of four ions and a two-dimensional crystal of 19 ions and verify the results, where possible, using other methods.The results show that the new method is an accurate and efficient tool for thermometry of ion crystals.
Coulomb crystals of cold trapped ions are a leading platform for the realisation of quantum processors and quantum simulations and, in quantum metrology, for the construction of optical atomic clocks and for fundamental tests of the Standard Model. For these applications, it is not only essential to cool the ion crystal in all its degrees of freedom down to the quantum ground state, but also to be able to determine its temperature with a high accuracy. However, when a large ground-state cooled crystal is interrogated for thermometry, complex many-body interactions take place, making it challenging to accurately estimate the temperature with established techniques. In this work we present a new thermometry method tailored for ion crystals. The method is applicable to all normal modes of motion and does not suffer from a computational bottleneck when applied to large ion crystals. We test the temperature estimate with two experiments, namely with a 1D linear chain of 4 ions and a 2D crystal of 19 ions and verify the results, where possible, using other methods. The results show that the new method is an accurate and efficient tool for thermometry of ion crystals.
We provide an introduction to the use of ion crystals in a Penning trap for experiments in quantum information. Macroscopic Penning traps allow for the containment of a few to a few million atomic ions whose internal states may be used in quantum information experiments. Ions are laser Doppler cooled, and the mutual Coulomb repulsion of the ions leads to the formation of crystalline arrays. The structure and dimensionality of the resulting ion crystals may be tuned using a combination of control laser beams and external potentials. We discuss the use of two-dimensional 9^{9}9Be+^{+}+ ion crystals for experimental tests of quantum control techniques. Our primary qubit is the 124 GHz ground-state electron spin flip transition, which we drive using microwaves. An ion crystal represents a spatial ensemble of qubits, but the effects of inhomogeneities across a typical crystal are small, and as such we treat the ensemble as a single effective spin. We are able to initialize the qubits in a simple state and perform a projective measurement on the system. We demonstrate full control of the qubit Bloch vector, performing arbitrary high-fidelity rotations ($\tau_{\pi}\sim$200 μ\muμs). Randomized Benchmarking demonstrates an error per gate (a Pauli-randomized π/2\pi/2π/2 and π\piπ pulse pair) of 8±1×10−48\pm1\times10^{-4}8±1×10−4. Ramsey interferometry and spin-locking measurements are used to elucidate the limits of qubit coherence in the system, yielding a typical free-induction decay coherence time of $T_{2}\sim$2 ms, and a limiting $T_{1\rho}\sim$688 ms. These experimental specifications make ion crystals in a Penning trap ideal candidates for novel experiments in quantum control. As such, we briefly describe recent efforts aimed at studying the error-suppressing capabilities of dynamical decoupling pulse sequences, demonstrating an ability to extend qubit coherence and suppress phase errors. We conclude with a discussion of future avenues for experimental exploration, including the use of additional nuclear-spin-flip transitions for effective multiqubit protocols, and the potential for Coulomb crystals to form a useful testbed for studies of large-scale entanglement.