Preparation of nonclassical states and measurement of the Wigner function for the collective motion of N trapped ions

We propose a scheme for generating nonclassical states for the centre-of-mass vibrational mode of N trapped ions,including superpositions of several coherent states on a circle and Fock states. In the scheme N trapped ions are driven by a laser beam tuned to the carrier. The scheme also provides a new prospect for laser cooling. The scheme can be used to measure the Wigner function of the collective vibrational mode.     

Generation of superpositions of coherent states of the motion of a trapped ion

We propose a method for preparing superpositions of coherent states of the motion of an ion in an anisotropic two-dimensional trap, in which the ion is tightly bound in the y direction. In the scheme the ion is excited by two resonant laser beams with equal amplitude, propagating along the x and y directions, respectively. In the Dicke-Lamb limit, an initial coherent state of the ion motion can be converted into a superposition of several coherent states on a circle through the laser-ion interactions and state-selective measurements on the ion. Received: 30 May 1997 / Revised: 29 July 1997 / Accepted: 22 October 1997     

制备囚禁离子的簇态

提出一个方案用于制备囚禁离子的簇态,制备过程中振动模仅仅是被虚激发。方案用双能级离子制备簇态,只要一束激光照射两个相互作用的离子。方案简单易行,成功几率可达到100.     

Cluster states prepared by using hot trapped ions

We propose a scheme for the preparation of one-dimensional and two-dimensional cluster states by using hot trapped ions. The scheme is based on the interaction between two ions and bichromatic radiation. The vibrational mode in our protocol is only virtually excited so that the system is insensitive to the thermal field. In addition, we only use two levels of ions as qubits and the successful probability may achieve 100%.     

Observing superpositions of different number states

The formal structure of quantum mechanics allows systems to exist in a superposition of different states. A curious feature is that while some superpositions, such as position or momentum, are routinely observed, others such as mass or charge are not. This anomaly is at least partly due to the fact that it is much easier to carry out interference experiments for certain observables than others. Here we focus particularly on the superposition of two different number states for photons or bosonic atoms. This can equally well be thought of as a superposition of different masses in the case of atoms. We present different interferometry schemes that should, at least in principle, allow us to observe interference between these states. This would provide evidence of a superposition that we would normally consider to be prevented by superselection rules.     

囚禁N2+离子的冷却实验

在Paul 阱中,开展了N2+离子电阻冷却和缓冲气体冷却实验。用抛出检测法精确测量离子信号的变化,提高了测量电阻冷却效果的灵敏度;用改变囚禁势的方法,测出了冷却离子的温度,观察到冷却离子的囚禁时间增加和速度分布范围减小的现象。     

Local transformations of superpositions of entangled states

Suppose that we have two entangled states |?₁〉, |ψ₁〉 that cannot be converted to any of other two states |?₂〉, |ψ₂〉 by local operations and classical communication. We analyze the possibility of locally transforming a superposition of |?₁〉 and |ψ₁〉 into a superposition of |?₂〉 and |ψ₂〉. By using the Nielsen's theorem we find the necessary and sufficient conditions for this conversion to be performed.     

Generation of long-living entanglement using cold trapped ions with pair cat states

With the reliance in the processing of quantum information on a cold trapped ion, we analyze the entanglement entropy in the ion-field interaction with pair cat states. We investigate a long-living entanglement allowing the instantaneous position of the center-of-mass motion of the ion to be explicitly time-dependent. An analytic solution for the system operators is obtained. We show that different nonclassical effects arise in the dynamics of the population inversion, depending on the initial states of the vibrational motion. We study in detail the entanglement degree and demonstrate how the input pair cat state is required for initiating the long-living entanglement. This long-living entanglement is damp out with an increase in the number difference q. Owing to the properties of entanglement measures, the results are checked using another entanglement measure (high order linear entropy). PACS 03.67.Nm; 03.65.Yz; 42.50.Dv     

Metastable superpositions of ortho- and para-Helium states

We analyze superpositions of ortho- and para-Helium states, considering the possible existence of stationary and metastable states in the system. In particular, the metastable superposition of 1s2s ortho- and para-states seems to be accessible to experimental scrutiny.     

Generation of displaced squeezed superpositions of coherent states

We study the method of generation of states that approximate superpositions of large-amplitude coherent states (SCSs) with high fidelity in free-traveling fields. Our approach is based on the representation of an arbitrary single-mode pure state, and SCSs in particular, in terms of displaced number states with an arbitrary displacement amplitude. The proposed optical scheme is based on alternation of photon additions and displacement operators (in the general case, N photon additions and N − 1 displacements are required) with a seed coherent state to generate both even and odd displaced squeezed SCSs regardless of the parity of the used photon additions. It is shown that the optical scheme studied is sensitive to the seed coherent state if the other parameters are unchanged. Output states can approximate either even squeezed SCS or odd SCS shifted relative to each other by some value. This allows constructing a local rotation operator, in particular, the Hadamard gate, which is a mainframe element for quantum computation with coherent states. We also show that three-photon additions with two intermediate displacement operators are sufficient to generate even displaced squeezed SCS with the amplitude 1.7 and fidelity more than 0.99. The effects deteriorating the quality of output states are considered.     

利用拉格朗日方程求解离子在分阱系统中的集体振动模式

介绍了利用拉格朗日方程求解离子在分阱系统中的集体振动模式的基本原理,并具体计算了分阱系统中3个离子的集体振动模式.     

Generation of pair coherent and cat states for the motion of two trapped ions

We propose a method for the generation of motional pair coherent states for the center of mass and relative motional modes for two trapped ions. The scheme is generalized to prepare pair cat states. The scheme does not require individual ionic laser addressing.     

Background-free detection of trapped ions

We demonstrate a Doppler cooling and detection scheme for ions with low-lying D levels which almost entirely suppresses scattered laser light background, while retaining a high fluorescence signal and efficient cooling. We cool a single ion with a laser on the $^{2}\mathrm{S}_{\mbox{\tiny$1/2$}}\leftrightarrow {^{2}\mathrm{P}}_{\mbox{\tiny$1/2$}}$ transition as usual, but repump via the $^{2}\mathrm{P}_{\mbox{\tiny$3/2$}}$ level. By filtering out light on the cooling transition and detecting only the fluorescence from the $^{2}\mathrm{P}_{\mbox{\tiny$3/2$}}\rightarrow {^{2}\mathrm{S}}_{\mbox{\tiny$1/2$}}$ decays, we suppress the scattered laser light background count rate to 1 s^?1 while maintaining a signal of 29000 s^?1 with moderate saturation of the cooling transition. This scheme will be particularly useful for experiments where ions are trapped in close proximity to surfaces, such as the trap electrodes in microfabricated ion traps, which leads to high background scatter from the cooling beam.     

Preparation and decoherence of superpositions of electromagnetic field states

In a recent experiment the progressive decoherence of a mesoscopic superposition of two coherent field states in a high-Q cavity, known as Schr?dinger cat state, has been measured for the first time [Brune et al., Phys. Rev. Lett. 77, 4887 (1996)]. Here, the full master equation governing the coupled dissipative dynamics of the atom-field system studied in the experiment is formulated and solved numerically for the experimental parameters. The model simulated avoids the approximations underlying an analytically solvable model which is based on a harmonic expansion of the energies of the dressed atomic states and on a treatment of their dynamics within the adiabatic approximation. In particular, the numerical simulations reveal that the coupling of the cavity field mode to its environment causes important decoherence effects already during the initial preparation phase of the Schr?dinger cat state. This phenomenon is investigated in detail with the help of a measure for the purity of states. Moreover, the Hilbert-Schmidt distance of the intended target state, the Schr?dinger cat, to the state that is actually prepared in the experiment is determined. Received 13 September 2000 and Received in final form 22 December 2000     

Generation of superpositions of coherent states on a circle

We propose a simple method to obtain a superposition of coherent states on a circle, including Schr?dinger cat states as a special case, via conditional measurement of the state of three level atoms interacting with a one mode cavity field. In the low amplitude limit, very good approximation of Fock states can also be generated in this way. Received: 8 October 1998 / Accepted: 30 October 1998     

Reconstruction of the two-mode vibronic quantum state of a trapped atom

We present a method for the direct measurement of the Wigner-function matrix for complex vibronic states of a trapped atom, that is suited to analyse the entanglement between two motional degrees of freedom and the internal electronic dynamics. It is a generalisation of the method for the determination of vibronic quantum states [S. Wallentowitz, R.L. de Matos Filho, W. Vogel, Phys. Rev. A 56, 1205 (1997)] in conjunction with the scheme for the direct observation of the Wigner function of a single motional degree of freedom [L.G. Lutterbach, L. Davidovich, Phys. Rev. Lett. 78, 2547 (1997)]. The major advantage of the present method is that it reduces the experimental efforts substantially. On the other hand, it is demonstrated that the nonlinear vibronic coupling necessary for this method turns out to be its main limitation. Received: 5 August 1998     

Inelastic scattering of heavy ions at intermediate energies with excitations of nuclear collective states

Excitation of low-lying nuclear collective states upon scattering of heavy ions with energies of several tens of MeV/nucleon has been studied. The interaction potential leading to excitation is chosen in the form of a derivative of the microscopic (or semimicroscopic) nucleus-nucleus double-folding optical potential. Elastic and inelastic scattering cross sections have been calculated within the high-energy approximation; the inelastic scattering amplitude was obtained in the first order in the deformation parameter. The cross sections are compared with the experimental data on scattering of ¹⁷O from a series of nuclei with excitation of the 2⁺ level.     

Teleportation of superpositions of macroscopic states of a cavity field

A scheme is presented for the teleportation of a superposition of two coherent states with equal amplitudes and opposite phases. It is based on a dispersive atom-cavity field interaction.