Hybrid Quantum Computing with Conditional Beam Splitter Gate in Trapped Ion System.

The hybrid approach to quantum computation simultaneously utilizes both discrete and continuous variables, which offers the advantage of higher density encoding and processing powers for the same physical resources. Trapped ions, with discrete internal states and motional modes that can be described by continuous variables in an infinite-dimensional Hilbert space, offer a natural platform for this approach. A nonlinear gate for universal quantum computing can be implemented with the conditional beam splitter Hamiltonian |e⟩⟨e|(a[over ^]^{†}b[over ^]+a[over ^]b[over ^]^{†}) that swaps the quantum states of two motional modes, depending on the ion's internal state. We realize such a gate and demonstrate its applications for quantum state overlap measurements, single-shot parity measurement, and generation of NOON states.

Quantum absorption refrigerator with trapped ions.

In recent years substantial efforts have been expended in extending thermodynamics to single quantum systems. Quantum effects have emerged as a resource that can improve the performance of heat machines. However in the fully quantum regime their implementation still remains a challenge. Here, we report an experimental realization of a quantum absorption refrigerator in a system of three trapped ions, with three of its normal modes of motion coupled by a trilinear Hamiltonian such that heat transfer between two modes refrigerates the third. We investigate the dynamics and steady-state properties of the refrigerator and compare its cooling capability when only thermal states are involved to the case when squeezing is employed as a quantum resource. We also study the performance of such a refrigerator in the single shot regime made possible by coherence and demonstrate cooling below both the steady-state energy and a benchmark set by classical thermodynamics.

Quantum Simulation with a Trilinear Hamiltonian.

Interaction among harmonic oscillators described by a trilinear Hamiltonian ℏξ(a^{†}bc+ab^{†}c^{†}) is one of the most fundamental models in quantum optics. By employing the anharmonicity of the Coulomb potential in a linear trapped three-ion crystal, we experimentally implement it among three normal modes of motion in the strong-coupling regime, where the coupling strength is much larger than the decoherence rate of the ion motion. We use it to simulate the interaction of an atom and light as described by the Tavis-Cummings model and the process of nondegenerate parametric down-conversion in the regime of a depleted pump.

Cross-Kerr Nonlinearity for Phonon Counting.

State measurement of a quantum harmonic oscillator is essential in quantum optics and quantum information processing. In a system of trapped ions, we experimentally demonstrate the projective measurement of the state of the ions' motional mode via an effective cross-Kerr coupling to another motional mode. This coupling is induced by the intrinsic nonlinearity of the Coulomb interaction between the ions. We spectroscopically resolve the frequency shift of the motional sideband of the first mode due to the presence of single phonons in the second mode and use it to reconstruct the phonon number distribution of the second mode.

Quantum Parametric Oscillator with Trapped Ions.

A strong nonlinear coupling between harmonic oscillators is highly desirable for quantum information processing and quantum simulation, but is difficult to achieve in many physical systems. Here, we exploit the Coulomb interaction between two trapped ions to achieve strong nonlinear coupling between normal modes of motion at the single-phonon level. We experimentally demonstrate phonon up- and down-conversion and apply this coupling to directly measure the parity and Wigner functions of the ions' motional states. Our results represent the fully quantum operation of a degenerate parametric oscillator and hold promise for quantum computation schemes that involve continuous variables.

Microwave control of trapped-ion motion assisted by a running optical lattice.

We experimentally demonstrate microwave control of the motional state of a trapped ion placed in a state-dependent potential generated by a running optical lattice. Both the optical lattice depth and the running lattice frequency provide tunability of the spin-motion coupling strength. The spin-motional coupling is exploited to demonstrate sideband cooling of a ^{171}Yb^{+} ion to the ground state of motion.

Narrow band source of transform-limited photon pairs via four-wave mixing in a cold atomic ensemble.

We observe narrow band pairs of time-correlated photons of wavelengths 776 and 795 nm from nondegenerate four-wave mixing in a laser-cooled atomic ensemble of ^{87}Rb using a cascade decay scheme. Coupling the photon pairs into single mode fibers, we observe an instantaneous rate of 7700 pairs per second with silicon avalanche photodetectors, and an optical bandwidth below 30 MHz. Detection events exhibit a strong correlation in time [g((2))(τ = 0) ≈ 5800] and a high coupling efficiency indicated by a pair-to-single ratio of 23%. The violation of the Cauchy-Schwarz inequality by a factor of 8.4 × 10(6) indicates a strong nonclassical correlation between the generated fields, while a Hanbury Brown-Twiss experiment in the individual photons reveals their thermal nature. The comparison between the measured frequency bandwidth and 1/e decay time of g((2)) indicates a transform-limited spectrum of the photon pairs. The narrow bandwidth and brightness of our source makes it ideal for interacting with atomic ensembles in quantum communication protocols.

Excitation of a single atom with exponentially rising light pulses.

We investigate the interaction between a single atom and optical pulses in a coherent state with a controlled temporal envelope. In a comparison between a rising exponential and a square envelope, we show that the rising exponential envelope leads to a higher excitation probability for fixed low average photon numbers, in accordance with a time-reversed Weisskopf-Wigner model. We characterize the atomic transition dynamics for a wide range of the average photon numbers and are able to saturate the optical transition of a single atom with ≈50 photons in a pulse by a strong focusing technique.

Preparation of an exponentially rising optical pulse for efficient excitation of single atoms in free space.

We report on a simple method to prepare optical pulses with exponentially rising envelope on the time scale of a few ns. The scheme is based on the exponential transfer function of a fast transistor, which generates an exponentially rising envelope that is transferred first on a radio frequency carrier, and then on a coherent cw laser beam with an electro-optical phase modulator. The temporally shaped sideband is then extracted with an optical resonator and can be used to efficiently excite a single (87)Rb atom.

Phase shift of a weak coherent beam induced by a single atom.

We report on a direct measurement of a phase shift on a weak coherent beam by a single 87Rb atom in a Mach-Zehnder interferometer. By strongly focusing the probe mode to the location of the atom, a maximum phase shift of about 1 degree is observed experimentally.