Using a displacement operator formalism, I analyse the depopulation of the vibrational ground state of trapped ions. Two heating times, one characterizing short time behaviour, the other long time behaviour are found. The short time behaviour is analyzed both for single and multiple ions, and a formula for the relative heating rates of different modes is derived. The possibility of correction of heating via the quantum Zeno effect, and the exploitation of the suppression of heating of higher modes to reduce errors in quantum computation is considered.
We describe the optimal realization of entangling quantum gates for trapped ions mediated by a dissipative bus mode. With suitably shaped control pulses one can substantially decrease ion-phonon entanglement while maintaining the mediated interaction.
We propose and demonstrate a scalable scheme for the simultaneous determination of internal and motional states in trapped ions with single-site resolution. The scheme is applied to the study of polaritonic excitations in the Jaynes- Cummings Hubbard model with trapped ions, in which the internal and motional states of the ions are strongly correlated. We observe quantum phase transitions of polaritonic excitations in two ions by directly evaluating their variances per ion site. Our work establishes an essential technological method for large-scale quantum simulations of polaritonic systems.
Invariant-based inverse engineering is an elegant approach to quantum control with corresponding experimental implementations that perform tasks with applications in quantum information processing such as shuttling trapped ions. We build on recent work to generalise invariant-based inverse engineering to control two coupled harmonic oscillators in any number of spatial dimensions. This may be used to perform experimentally relevant tasks such as separation of trapped ions, which is demonstrated numerically, achieving transfer fidelities of over 96% as well as low motional number excitations.
Essentially all known quantum gates rely on a weak-coupling approximation resulting in linear dynamics. With the explicit example of trapped ions, we show how high-fidelity quantum gates can be achieved outside such an approximation, and we derive readily implementable driving fields to realize gates with extremely high fidelities for ions well outside the Lamb-Dicke regime with motional temperatures achievable by only Doppler cooling.
We propose a method to manipulate the normal modes in a chain of trapped ions using only two lasers. Linear chains of trapped ions have proven experimentally to be highly controllable quantum systems with a variety of refined techniques for preparation, evolution, and readout, however, typically for quantum information processing applications people have been interested in using the internal levels of the ions as the computational basis. We analyse the case where the motional degrees of freedom of the ions is the quantum system of interest, and where the internal levels are leveraged to facili…
Simulation of Jahn-Teller-Dicke Magnetic Structural Phase Transition with Trapped Ions
本文从理论上研究了囚禁离子系统中的集体E $\otimes$ e Jahn-Teller-Dicke畸变。我们的重点是在无限范围内的相互作用，其中有效自旋系综与两个集体振动模式与U（1）对称耦合的限制。我们的模型是完全可解的结晶极限，它是适合于解决一个中等数量的离子的精确数值对角化。我们发现，被困离子是理想的适合研究出现的连续对称性和磁结构相变在介观系统的自发对称性破缺。
We show how to produce a fast quantum Rabi model with trapped ions. Its importance resides not only in the acceleration of the phenomena that may be achieved with these systems, from quantum gates to the generation of nonclassical states of the vibrational motion of the ion, but also in reducing unwanted effects such as the decay of coherences that may appear in such systems.
We apply estimation theory to a system formed by two interacting trapped ions. By using the Fisher matrix formalism, we introduce a simple scheme for estimation of the temperature of the longitudinal vibrational modes of the ions. We use the ions interaction to effectively infer the temperature of the individual ions, by optimising the interaction time evolution and by measuring only over one of the ions. We also investigate the effect of a non-thermal reservoir over the inference approach. The non-classicality of one of the ions vibrational modes, introduced due to a squeezed thermal reservoi…
We have experimentally observed the dynamics of a single polariton and two polaritons in a two-ion chain. By driving two trapped ions at a motional blue-sideband transition, we realize the anti-Jaynes-Cummings-Hubbard model. When a single polariton exists in a trapped-ion chain, the polariton hops between the ion sites. On the other hand, when there are single polaritons at each ion site, the hopping of the polaritons is suppressed because of the polariton-polariton interaction induced by the nonlinearity of the anti-Jaynes-Cummings interaction, thereby realizing the blockade of polariton hopp…
In this paper, we present a dynamical decoupling (DD) technique to coherently control the dynamics of a single local phonon in trapped ions. A 2$π$ rotation at a motional sideband transition flips the sign of the relevant local phonon state, resulting in cancellation of the phonon dynamics. In this work, we implement DD using single and multiple blue-sideband pulses to control a single local phonon in two $^{40}{\rm Ca}^{+}$ ions in a linear Paul trap. Our proposed DD technique can be used to engineer coupling between local phonon modes.
Engineering the unitary charge-conjugation operator of quantum field theory for particle-antiparticle using trapped ions and light fields in cavity QED
