Observation of Hopping and Blockade of Bosons in a Trapped Ion Spin Chain

Abstract

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 opens up the possibility of realizing large-scale Hubbard systems from the bottom up with tunable interactions at the single-site level.Trapped atomic ions are an excellent medium for quantum computation and quantum simulation, acting as a many-body system of spins with programmable and reconfigurable Ising couplings [1][2][3]. In this system, the long-range spin-spin interaction is mediated by the collective motion of an ion chain and emerges over time scales longer than the propagation time of mechanical waves or phonons through the crystal [4,5]. On the other hand, at shorter timescales, such a chain represents a bosonic system of phonon modes that describe the local motion of individual ions. Here each local mode is defined by the harmonic confinement of a particular ion with all other ions pinned. In this picture, phonons hop between the local modes due to the long-range Coulomb interaction between ions [6][7][8]. This intrinsic hopping in trapped ion crystals makes it a viable candidate for simulating manybody systems of bosons [6,7], boson interference [9] and applications such as boson sampling [10].Such a system of local oscillators can be approximated to the lowest order of the transverse ion displacement by the phonon Hamiltonian (h = 1),Here the local mode frequency of each ion is expressed as a sum of the common mode transverse trap frequency ω x and a position-dependent frequency shift ω j experienced by the j−th ion [6,7]. The local mode bosonic creation and annihilation operators are a † j and a j , respectively. The long-range hopping term κ jk = e 2 /(2M ω x d 3 jk ) is determined by the distance d jk between ions j and k, where e and M are the charge and mass of a single ion.By applying external controls to the system, on-site interactions between phonons lead to the simulation of Hubbard models of bosons. For instance, applied position-dependent Stark shifts can result in effective phonon-phonon interactions [6]. Combined with phonon hopping between sites, such a system follows the BoseHubbard model. In the approach considered here, the internal spin is coupled to the external phonon mode by driving the spin resonance on a motion-induced sideband transition [11]. This gives rise to nonlinear onsite interactions between spin-phonon excitations (polaritons). Such a system simulates the Jaynes-CummingsHubbard model, which describes an array of coupled cavities [7,8,[12][13][14].In order to study the dynami...

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