L. F. Wei

Quantum entanglement and quantum squeezing are two most typical approaches to beat the standard quantum limit (SQL) of the sensitive phase estimations in quantum metrology. Each of them has already been utilized individually to improve the sensitivity of electric field sensing with the trapped ion platform, but the upper bound of the demonstrated sensitivity gain is very limited, i.e., the experimental 3dB and theoretical 6dB, over the SQL. Here, by simultaneously using the internal (spin)-external (oscillator) state entanglements and the oscillator squeezings to effectively amplify the accumulation phase, we show that these sensitivity gains can be effectively surpassed. Hopefully, the proposal provides a novel approach to the stronger beaten of the SQL for the sensitive sensings of the desired electric field and also the other metrologies.

An approach is proposed to implement the universal quantum gates between the ions confined individually in the separated traps. Instead of the typical adiabatic operations, performed for manipulating the ion-ion coupling, here the switchable couplings between ions are implemented non-adiabatically by using the fast laser pulses. Consequently, the desirable quantum gates between the ions could be implemented by using only a series of laser pulses. The proposal may be conveniently generalized to the quantum computation with the scalable ion-traps.

Recent experiments [K. R. Brown, et al., Nature 471, 196 (2011); and M. Harlander, et al., Nature 471, 200 (2011)] have demonstrated the coherent manipulations on the external vibrations of two ions, confined individually in the separated ion traps. Using these recently developed techniques, we propose here an approach to realize the coherent operations, e.g., the universal quantum gates, between the separated ion-trap qubits encoded by two internal atomic states of the trapped ions. Our proposal operates beyond the usual Lamb-Dicke limits, and could be applied to the scalable ion traps coupled by their vibrations.

Entangling multiple qubits is one of the central tasks for quantum information processings. Here, we propose an approach to entangle a number of cold ions (individually trapped in a string of microtraps) by a moved cavity. The cavity is pushed to include the ions one by one with an uniform velocity, and thus the information stored in former ions could be transferred to the latter ones by such a moving cavity bus. Since the positions of the trapped ions are precisely located, the strengths and durations of the ion-cavity interactions can be exactly controlled. As a consequence, by properly setting the relevant parameters typical multi-ion entangled states, e.g., $W$ state for 10 ions, could be deterministically generated. The feasibility of the proposal is also discussed.

Jaynes-Cummings model is a typical model in quantum optics and has been realized with various physical systems (e.g, cavity QED, trapped ions, and circuit QED etc..) of two-level atoms interacting with quantized bosonic fields. Here, we propose a new implementation of this model by using a single classical laser beam to drive an electron floating on liquid Helium. Two lowest levels of the {\it vertical} motion of the electron acts as a two-level "atom", and the quantized vibration of the electron along one of the {\it parallel} directions, e.g., $x$-direction, serves the bosonic mode. These two degrees of freedom of the trapped electron can be coupled together by using a classical laser field. If the frequencies of the applied laser fields are properly set, the desirable Jaynes-Cummings models could be effectively realized.

For certain {\it specific} (or {\it"magic"}) Lamb-Dicke (LD) parameters, Monroe {\it et al} showed [Phys. Rev. {\bf A 55}, R2489 (1997)] that a two-qubit quantum operation, between the external and internal degrees of freedom of a single trapped ion, could be implemented by applying a single carrier laser pulse. Here, we further show that, such a two-qubit operation (which is equivalent to the standard CNOT gate, only apart from certain phase factors) could also be significantly-well realized for {\it arbitrarily} selected LD parameters. Instead of the so-called "$π$-pulses" used in the previous demonstrations, the durations of the pulses applied in the present proposal are required to be accurately set within the decoherence times of the ion. % We also propose a simple approach by using only one off-resonant (e.g., blue-sideband) laser pulse to eliminate the unwanted phase factors existed in the above two-qubit operations for generating the standard CNOT gates.

Exploiting the intrinsic nonlinearity of superconducting Josephson junctions, we propose a scalable circuit with superconducting qubits (SCQs) which is very similar to the successful one now being used for trapped ions. The SCQs are coupled to the "vibrational" mode provided by a superconducting LC circuit or its equivalent (e.g., a SQUID). Both single-qubit rotations and qubit-LC-circuit couplings/decouplings can be controlled by the frequencies of the time-dependent magnetic fluxes. The circuit is scalable since the qubit-qubit interactions, mediated by the LC circuit, can be selectively performed, and the information transfer can be realized in a controllable way.

Based on the exact conditional quantum dynamics for a two-ion system, we propose an efficient {\it single-step} scheme for coherently manipulating quantum information of two trapped cold ions by using a pair of synchronous laser pulses. Neither the auxiliary atomic level nor the Lamb-Dicke approximation are needed.

We propose an effective scheme for manipulating quantum information stored in a superconducting nanocircuit. The Josephson qubits are coupled via their separate interactions with an information bus, a large current-biased Josephson junction treated as an oscillator with adjustable frequency. The bus is sequentially coupled to only one qubit at a time. Distant Josephson qubits without any direct interaction can be indirectly coupled with each other by independently interacting with the bus sequentially, via exciting/de-exciting vibrational quanta in the bus. This is a superconducting analog of the successful ion trap experiments on quantum computing. Our approach differs from previous schemes that simultaneously coupled two qubits to the bus, as opposed to their sequential coupling considered here. The significant quantum logic gates can be realized by using these tunable and selective couplings. The decoherence properties of the proposed quantum system are analyzed within the Bloch-Redfield formalism. Numerical estimations of certain important experimental parameters are provided.

Based on the conditional quantum dynamics of laser-ion interaction, we propose an efficient theoretical scheme to deterministically generate quantum pure states of a single trapped cold ion without performing the Lamb-Dicke approximation. An arbitrary quantum state can be created by using a series of classical laser beams with selected frequencies, initial phases and durations. As special examples, we further show how to create or approximate several typical macroscopic quantum states, such as the phase state and (even/odd) coherent states. Unlike previous schemes operated in the Lamb-Dicke regime, the present one does well for arbitrary strength coupling between the internal and external degrees of freedom of the ion. The experimental realizability of this approach is also discussed.

A simple alternative scheme for implementing quantum gates with a single trapped cold two-level ion beyond the Lamb-Dicke (LD) limit is proposed. Basing on the quantum dynamics for the laser-ion interaction described by a generalized Jaynes-Cummings model, one can introduce two kinds of elementary quantum operations i.e., the simple rotation on the bare atomic state, generated by applying a resonant pulse, and the joint operation on the internal and external degrees of the ion, performed by using an off-resonant pulse. Several typical quantum gates, including Hadamard gate, controlled-Z and controlled-NOT gates $etc.$, can thus be implemented exactly by using these elementary operations. The experimental parameters including the LD parameter and the durations of the applied laser pulses, for these implementation are derived analytically and numerically. Neither the LD approximation for the laser-ion interaction nor the auxiliary atomic level is needed in the present scheme.

We propose a simple scheme for implementing quantum logic gates with a string of two-level trapped cold ions outside the Lamb-Dicke limit. Two internal states of each ion are used as one computational qubit (CQ) and the collective vibration of ions acts as the information bus, i.e., bus qubit (BQ). Using the quantum dynamics for the laser-ion interaction as described by a generalized Jaynes-Cummings model, we show that quantum entanglement between any one CQ and the BQ can be coherently manipulated by applying classical laser beams. As a result, universal quantum gates, i.e. the one-qubit rotation and two-qubit controlled gates, can be implemented exactly. The required experimental parameters for the implementation, including the Lamb-Dicke (LD) parameter and the durations of the applied laser pulses, are derived. Neither the LD approximation for the laser-ion interaction nor the auxiliary atomic level is needed in the present scheme.