We propose a scheme to implement quantum gates on any pair of trapped ions immersed in a large linear crystal, using interaction mediated by the transverse phonon modes. Compared with the conventional approaches based on the longitudinal phonon modes, this scheme is much less sensitive to ion heating and thermal motion outside of the Lamb-Dicke limit thanks to the stronger confinement in the transverse direction. The cost for such a gain is only a moderate increase of the laser power to achieve the same gate speed. We also show how to realize arbitrary-speed quantum gates with transverse phonon modes based on simple shaping of the laser pulses.
Driving an ion at a motional sideband transition induces the Jaynes--Cummings (JC) interaction. This JC interaction creates an anharmonic ladder of JC eigenstates, resulting in the suppression of phonon hopping due to energy conservation. Here, we realize phonon blockade in the presence of multiple local phonons in a trapped-ion chain. Our work establishes a key technological component for quantum simulation with multiple bosonic particles, which can simulate classically intractable problems.
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.
Quantum manipulation of individual phonons could offer new resources for studying fundamental physics and creating an innovative platform in quantum information science. Here, we propose to generate quantum states of strongly correlated phonon bundles associated with the motion of a trapped atom. Our scheme operates in the atom-phonon resonance regime where the energy spectrum exhibits strong anharmonicity such that energy eigenstates with different phonon numbers can be well-resolved in the parameter space. Compared to earlier schemes operating in the far dispersive regime, the bundle states …
Propagation and interference of quantum-mechanical particles comprise an important part of elementary processes in quantum physics, and their essence can be modeled using a quantum walk, a mathematical concept that describes the motion of a quantum-mechanical particle among discretized spatial regions. Here we report the observation of the quantum walks of a phonon, a vibrational quantum, in a trapped-ion crystal. By employing the capability of preparing and observing a localized wave packet of a phonon, the propagation of a single radial local phonon in a four-ion linear crystal is observed w…
We show that a trapped ion chain interacting with an optical spin-dependent force shows strong frustration effects due to the interplay between long-range interactions and the dressing by optical phases. We consider a strong spin-phonon coupling regime and predict a quantum phase diagram with different competing magnetic and structural orders. In a highly frustrated region, the system shows enhanced quantum fluctuations and entanglement characteristic of spin-liquid phases. We propose and describe within a mean-field approach a quantum annealing process to induce a quasi-adiabatic evolution to…
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…
Trapped ions offer a pristine platform for quantum computation and simulation, but improving their coherence remains a crucial challenge. Here, we propose and analyze a new strategy to enhance the coherent interactions in trapped ion systems via parametric amplification of the ions' motion--by squeezing the collective motional modes (phonons), the spin-spin interactions they mediate can be significantly enhanced. We illustrate the power of this approach by showing how it can enhance collective spin states useful for quantum metrology, and how it can improve the speed and fidelity of two-qubit …
We propose a tunable phonon laser prototype with a large trapped ion array, where some of the ions are effectively pinned by optical tweezers, thus isolating a subset of ions that mimics an acoustic cavity used as a phonon lasing resonator. The cavity loss can then be controlled by the tweezer strength and the "wall thickness", the number of pinned ions for isolation. We pump the resonator by applying blue-sideband lasers, and investigate the lasing dynamics of the cavity modes such as threshold behavior, population distribution, the second-order coherence, and line-narrowed spectrum. This sch…
A method for gaining information about the phonon-number moments and the generalized nonlinear and linear quadratures in the motion of trapped ions (in particular, position and momentum) is proposed, valid inside and outside the Lamb-Dicke regime. It is based on the measurement of first time derivatives of electronic populations, evaluated at the motion-probe interaction time t=0. In contrast to other state-reconstruction proposals, based on measuring Rabi oscillations or dispersive interactions, the present scheme can be performed resonantly at infinitesimal short motion-probe interaction tim…
We present a novel system for the simulation of quantum phase transitions of collective internal qubit and phononic states with a linear crystal of trapped ions. The laser-ion interaction creates an energy gap in the excitation spectrum, which induces an effective phonon-phonon repulsion and a Jaynes-Cummings-Hubbard interaction. This system shows features equivalent to phase transitions of polaritons in coupled cavity arrays. Trapped ions allow for easy tunabilty of the hopping frequency by adjusting the axial trapping frequency, and the phonon-phonon repulsion via the laser detuning and inte…
Two-photon processes have so far been considered only as resulting from frequency-matched second-order expansions of light-matter interaction, with consequently small coupling strengths. However, a variety of novel physical phenomena arises when such coupling values become comparable with the system characteristic frequencies. Here, we propose a realistic implementation of two-photon quantum Rabi and Dicke models in trapped-ion technologies. In this case, effective two-phonon processes can be explored in all relevant parameter regimes. In particular, we show that an ion chain under bichromatic…
We propose and demonstrate phonon-number-resolving detection of the multiple local phonon modes in a trapped-ion chain. To mitigate the effect of phonon hopping during the detection process, the probability amplitude of each local phonon mode is mapped to the auxiliary long-lived motional ground states. Sequential state-dependent fluorescence detection is then performed. In the experiment, we have successfully observed the time evolution of two local phonon modes in two ions, including the phonon-number correlation between the two modes.
We demonstrate tunable spin-spin couplings between trapped atomic ions, mediated by laser forces on multiple transverse collective modes of motion. A $σ_x σ_x$-type Ising interaction is realized between quantum bits stored in the ground hyperfine clock states of Yb ions. We demonstrate entangling gates and tailor the spin-spin couplings with two and three trapped ions. The use of closely-spaced transverse modes provides a new class of interactions relevant to quantum computing and simulation with large collections of ions in a single crystal.
Stochastic cooling of trapped atoms is considered for a laser-beam configuration with beam waists equal or smaller than the extent of the atomic cloud. It is shown, that various effects appear due to this transverse confinement, among them heating of transverse kinetic energy. Analytical results of the cooling in dependence on size and location of the laser beam are presented for the case of a non-degenerate vapour.
We propose an experimental architecture where an array of optical tweezers affords site-dependent control over the confining potential of a conventional radio-frequency ion trap. The site-dependent control enables programmable manipulation of phonon modes of ions, with many potential applications in quantum information processing (QIP) and thermodynamics. We describe protocols for programming the array of optical tweezers to attain a set of target phonon modes with high accuracy. We propose applications of such controls in simulating quantum thermodynamics of a particle of programmable effecti…
We show how to generate quadratic and bi-quadratic phonon-photon interactions through a driven three-level ion inside a cavity. With such a system it is possible to squeeze the cavity-field state, the ion motional state or even the entangled phonon-photon state. We present a detailed analysis of the cavity-field squeezing process, distinguishing three different regimes of this amplification mechanism: the subcritical, critical, and supercritical regimes, which depend, apart from the coupling parameters, on the excitation of the vibrational state. As an application of the engineered Hamiltonian…
We examine in detail the theory of the intrinsic non-linearities in the dynamics of trapped ions due to the Coulomb interaction. In particular the possibility of mode-mode coupling, which can be a source of decoherence in trapped ion quantum computation, or, alternatively, can be exploited for parametric down-conversion of phonons, is discussed and conditions under which such coupling is possible are derived.
In this paper we propose a scheme to model the phonon analog of optical elements, including a polarizing beam splitter, a half- wave plate, and a quarter- wave plate, as well as an implementation of CNOT and Pauli gates, by using two atoms confined in a 2D plane. The internal states of the atoms are taken to be Rydberg circular states. Using this model we can manipulate the motional state of the atom, with possible applications in optomechanical integrated circuits for quantum information processing and quantum simulation. Towards this aim, we study the interaction of two trapped atoms with tw…
We propose a protocol for measurement of the phonon number distribution of a harmonic oscillator based on selective mapping to a discrete spin-1/2 degree of freedom. We consider a system of a harmonically trapped ion, where a transition between two long lived states can be driven with resolved motional sidebands. The required unitary transforms are generated by amplitude-modulated polychromatic radiation fields, where the time-domain ramps are obtained from numerical optimization by application of the Chopped RAndom Basis (CRAB) algorithm. We provide a detailed analysis of the scaling behavior…
In trapped-ion quantum information processing, interactions between spins (qubits) are mediated by collective modes of motion of an ion crystal. While there are many different experimental strategies to design such interactions, they all face both technical and fundamental limitations to the achievable coherent interaction strength. In general, obtaining strong interactions and fast gates is an ongoing challenge. Here, we extend previous work [Phys. Rev. Lett. 112, 030501 (2019)] and present a general strategy for enhancing the interaction strengths in trapped-ion systems via parametric amplif…
The local phonon modes in a Coulomb crystal of trapped ions can represent a Hubbard system of coupled bosons. We selectively prepare single excitations at each site and observe free hopping of a boson between sites, mediated by the long-range Coulomb interaction between ions. We then implement phonon blockades on targeted sites by driving a Jaynes-Cummings interaction on individually addressed ions to couple their internal spin to the local phonon mode. The resulting dressed states have energy splittings that can be tuned to suppress phonon hopping into the site. This new experimental approach…
We investigate quantum synchronization theoretically in a system consisting of two cold ions in microtraps. The ions' motion is damped by a standing-wave laser whilst also being driven by a blue-detuned laser which results in self-oscillation. Working in a non-classical regime, where these oscillations contain only a few phonons and have a sub-Poissonian number variance, we explore how synchronization occurs when the two ions are weakly coupled using a probability distribution for the relative phase. We show that strong correlations arise between the spin and vibrational degrees of freedom wit…
The vibrations of a chain of trapped ions can be considered, under suitable experimental conditions, as an ensemble of interacting phonons, whose quantum dynamics is governed by a Bose--Hubbard Hamiltonian. In this work we study the quantum phases which appear in this system, and show that thermodynamical properties, such as critical parameters and critical exponents, can be measured in experiments with a limited number of ions. Besides that, interacting phonons in trapped ions offer us the possibility to access regimes which are difficult to study with ultracold bosons in optical lattices, li…
The interaction between the electric dipole moment of a trapped molecular ion and the configuration of the confined Coulomb crystal couples the orientation of the molecule to its motion. We consider the practical feasibility of harnessing this interaction to initialize, process, and read out quantum information encoded in molecular ion qubits without optically illuminating the molecules. We present two schemes wherein a molecular ion can be entangled with a co-trapped atomic ion qubit, providing, among other things, a means for molecular state preparation and measurement. We also show that vir…
We analyse a protocol of quantum energy teleportation that transports energy from the left edge of a linear ion crystal to the right edge by local operations and classical communication at a speed considerably greater than the speed of a phonon in the crystal. A probe qubit is strongly coupled with phonon fluctuation in the ground state for a short time, and it is projectively measured in order to obtain information about this phonon fluctuation. During the measurement process, phonons are excited by the time-dependent measurement interaction, and the energy of the excited phonons must be infu…
We study two trapped ions coupled to the axial phonon modes of a one-dimensional Coulomb crystal. This system is formally equivalent to the "two spin-boson" model. We propose a scheme to dynamically generate a maximally entangled state of two ions within a decoherence-free subspace. Here the phononic environment of the trapped ions, whatever its temperature and number of modes, serves as the entangling bus. The efficient production of the pure singlet state can be exploited to perform short-ranged quantum communication which is essential in building up a large-scale quantum computer.
We theoretically investigate the possibility of creating phonon-mediated spin-spin interactions between neutral atoms trapped in optical tweezers. By laser coupling the atoms to Rydberg states, collective modes of motion appear. We show that these can be used to mediate effective spin-spin interactions or quantum logic gates between the atoms in analogy to schemes employed in trapped ions. In particular, we employ Rydberg dressing in a novel scheme to induce the needed interaction, and we show that it is possible to replicate the working of the Mølmer-Sørensen entanglement scheme. The Mølmer-S…
We propose an adiabatic method for optimal phonon temperature estimation using trapped ions which can be operated beyond the Lamb-Dicke regime. The quantum sensing technique relies on a time-dependent red-sideband transition of phonon modes, described by the non-linear Jaynes-Cummings model in general. A unique feature of our sensing technique is that the relevant information of the phonon thermal distributions can be transferred to the collective spin-degree of freedom. We show that each of the thermal state probabilities is adiabatically mapped onto the respective collective spin-excitation …
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 present a self-contained operator-based approach to derive the spectrum of trapped ions. This approach provides the complete normal form of the low energy quadratic Hamiltonian in terms of bosonic phonons, as well as an effective free particle degree of freedom for each spontaneously broken spatial symmetry. We demonstrate how this formalism can directly be used to characterize an ion chain both in the linear and the zigzag regimes. In particular we compute, both for the ground state and finite temperature states, spatial correlations, heat capacity and dynamical susceptibility. Last, for t…
The vibrations of a collection of ions in a microtrap array can be described in terms of hopping phonons. We show theoretically that the vibrational couplings may be tailored by using a gradient of the microtrap frequencies, together with a periodic driving of the trapping potential. These ingredients allow us to induce effective gauge fields on the vibrational excitations, such that phonons mimic the behavior of charged particles in a magnetic field. In particular, microtrap arrays are ideally suited to realize the famous Aharonov-Bohm effect, and observe the paradigmatic edge states typical …
Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences（中国科学院精密测量科学与技术创新研究院）；University of the Chinese Academy of Sciences（中国科学院大学）；College of Science, National University of Defense Technology（国防科技大学理学院）
We propose a concrete experiment to probe the non-equilibrium local dynamics of the one-dimensional Bose-Hubbard model using a trapped ion system consisting of a linear chain of few Ba^+ ions prepared in a state of transverse motional mode which corresponds to a fixed number of phonons per ion. These phonons are well-known to be described by an effective Bose-Hubbard model. We propose a protocol which leads to a sudden local sign reversal of the on-site interaction strength of this Hubbard model at one of the sites and demonstrate that the subsequent non-equilibrium dynamics of the model can b…
Non-Hermitian skin effect (NHSE) describes the exponential localization of all eigenstates toward boundaries in non-Hermitian systems, and has attracted intense research interest of late. Here we theoretically propose a scheme in which the NHSE significantly impacts the external motion of a single trapped ion through complex spin-motion dynamics. On the one hand, we show the competition between the NHSE and the coherent Bloch dynamics. On the other hand, since the NHSE manifests as a non-reciprocal flow in occupied phonon modes, we demonstrate that such dynamics can have potential applications…
We introduce quantum sensing protocol for detection spatially varying fields by using two coupled harmonic oscillators as a quantum probe. We discuss a physical implementation of the sensing technique with two trapped ions coupled via Coulomb mediated phonon hopping. Our method relies on using the coupling between the localized ion oscillations and the internal states of the trapped ions which allows to measure spatially varying electric and magnetic fields. First we discuss an adiabatic sensing technique which is capable to detect a very small force difference simply by measuring the ion spin…
Linear Paul traps have been used recently to simulate the transverse field Ising model with long-range spin-spin couplings. We study the intrinsic effects of phonon creation (from the initial phonon ground state) on the spin-state probability and spin entanglement for such quantum spin simulators. While it has often been assumed that phonon effects are benign because they play no role in the pure Ising model, they can play a significant role when a transverse field is added to the model. We use a many-body factorization of the quantum time-evolution operator of the system, adiabatic perturbati…
Qubits of long coherence time and fast quantum operations are long-sought objectives towards the realization of high-fidelity quantum operations and their applications to the quantum technologies. An electron levitated in a vacuum by a Paul trap is expected to be a good candidate, for its light mass and hence the high secular frequency which allows for the faster gate operations than those in trapped ions. Controlling the motional state of the trapped electron is a crucial issue, for it mediates an interaction between electron spins, intrinsic qubits embedded in electrons, and its decoherence …
