The quantum statistics of bosons and fermions manifest themselves in the manner in which two indistinguishable particles interfere quantum mechanically. When two photons, which are bosonic particles, enter a beam-splitter with one photon in each input port, they bunch together at either of the two output ports. The corresponding disappearance of the coincidence count is the Hong-Ou-Mandel effect. Here we show the phonon counterpart of this effect in a system of trapped-ion phonons, which are collective excitations derived by quantizing vibrational motions that obey Bose-Einstein statistics. We realize a beam-splitter transformation of the phonons by employing the mutual Coulomb repulsion between ions, and perform a two-phonon quantum interference experiment using that transformation. We observe an almost perfect disappearance of the phonon coincidence between two ion sites, confirming that phonons can be considered indistinguishable bosonic particles. The two-particle interference demonstrated here is purely a quantum effect, without a classical counterpart, hence it should be possible to demonstrate the existence of entanglement on this basis. We attempt to generate an entangled state of phonons at the centre of the Hong-Ou-Mandel dip in the coincidence temporal profile, under the assumption that the entangled phonon state is successfully generated if the fidelity of the analysis pulses is taken into account adequately. Two-phonon interference, as demonstrated here, proves the bosonic nature of phonons in a trapped-ion system. It opens the way to establishing phonon modes as carriers of quantum information in their own right, and could have implications for the quantum simulation of bosonic particles and analogue quantum computation via boson sampling.

We report an experimental realization of the Jaynes-Cummings-Hubbard model using the internal and radial phonon states of two trapped ions. An adiabatic transfer corresponding to a quantum phase transition from a localized insulator ground state to a delocalized superfluid (SF) ground state is demonstrated. The SF phase of polaritonic excitations characteristic of the interconnected Jaynes-Cummings (JC) system is experimentally explored, where a polaritonic excitation refers to a combination of an atomic excitation and a phonon interchanged via a JC coupling.

Quantum tunnelling is a common fundamental quantum mechanical phenomenon that originates from the wave-like characteristics of quantum particles. Although the quantum tunnelling effect was first observed 85 years ago, some questions regarding the dynamics of quantum tunnelling remain unresolved. Here we realize a quantum tunnelling system using two-dimensional ionic structures in a linear Paul trap. We demonstrate that the charged particles in this quantum tunnelling system are coupled to the vector potential of a magnetic field throughout the entire process, even during quantum tunnelling, as indicated by the manifestation of the Aharonov-Bohm effect in this system. The tunnelling rate of the structures periodically depends on the strength of the magnetic field, whose period is the same as the magnetic flux quantum f 0 through the rotor [(0.99±0.07) Â f 0 ].

Universal single-qubit operations based on purely geometric phase factors in adiabatic processes are demonstrated by utilizing a four-level system in a trapped single $^{40}$Ca$^+$ ion connected by three oscillating fields. Robustness against parameter variations is studied. The scheme demonstrated here can be employed as a building block for large-scale holonomic quantum computations, which may be useful for large qubit systems with statistical variations in system parameters

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We report a linear surface-electrode trap that can be used to form parallel ion strings. By adjusting the balance of the radio-frequency (RF) voltages applied to central and RF electrodes, the RF pseudopotential can be varied from single-well to double-well in the radial direction. Ions located on two parallel lines of the RF potential null are in principle free from excess micromotion if appropriate static voltages are applied. Calcium ions were trapped for the evaluation of the designed electrode. An ion string in the single-well potential and two ion strings in the double-well potential were observed by changing the RF voltages. Such traps could be used for quantum simulation of coupled spin systems.

We generate half-excited symmetric Dicke states of two and four ions. We use multilevel stimulated Raman adiabatic passage whose intermediate states are phonon Fock states. This process corresponds to the spin squeezing operation and half-excited Dicke states are generated during multilevel stimulated Raman adiabatic passage. This method does not require local access for each ion or the preparation of phonon Fock states. Furthermore, it is robust since it is an adiabatic process. We evaluate the Dicke state using a witness operator and determine the upper and lower bounds of the fidelity without using full quantum tomography.