Multiparticle Entanglement of Hot Trapped Ions

Abstract

We propose an efficient method to produce multi-particle entangled states of ions in an ion trap for which a wide range of interesting effects and applications have been suggested. Our preparation scheme exploits the collective vibrational motion of the ions, but it works in such a way that this motion need not be fully controlled in the experiment. The ions may, e.g., be in thermal motion and exchange mechanical energy with a surrounding heat bath without detrimental effects on the internal state preparation. Our scheme does not require access to the individual ions in the trap.

An efficient single-step scheme for manipulating quantum information of two trapped ions beyond the Lamb–Dicke limit

“…Jefferts et al [27] point out that applying a static electric field to push the ions along x may control the amplitude of ξ j and thus the Ω j of the ion micro-motion. Finally, we note that the duration of the two applied simultaneous pulses for realizing the above quantum controlled operation is not much longer than that for other schemes (see, e.g., [5,9,12,17]) operating in the LD regime. The shortest duration of the applied synchronous pulses for realizing the above manipulations of two trapped ions is about 10 −4 seconds, of the same order of the gate speed operating in the LD regime [8], for Ω 1 /2π ≈ 225 kHz [10].…”

“…Thus, hereafter we neglect all off-resonant transitions and the excitations of the higher vibrational modes [23,24,25], i.e., let F j =Î, and only label the CM mode excitations. We stress the following important fact: the effective Hamiltonian (3) reduces to that in previous works (e.g., [5,9,12,17] under the usual LD approximation: (m+ 1)η 2 j ≪ 1), to the lowest order of the LD parameter η j . Here m is the occupation number of the Fock state of the CM vibrational quanta.…”

“…In the past few years, several key features of the proposal in [6], including the production of entangled states and the implementation of quantum controlled operations between a pair of trapped ions, have already been experimentally demonstrated * lfwei@riken.jp † fnori@riken.jp ‡ Permanent address [5,8,9,10]. Also, several alternative theoretical schemes (see, e.g., [11,12,13,14,15,16,17]) have been developed for overcoming various difficulties in realizing a practical iontrap quantum information processor.…”

“…The Lamb-Dicke (LD) approximation is made in almost all of these schemes (see, e.g., [5,9,12,16,17]), in order to simplify the treatment of the laser-ion interaction. This approximation requires that the coupling between the external and internal degrees of freedom of the ion is very weak, i.e., the spatial dimension of the motion of the ground state of the trapped ion should be much smaller than the effective wavelength of the applied laser field (see, e.g., [18]).…”

Fast geometric gate operation of superconducting charge qubits in circuit QED

“…So, how to suppress this infamous decoherence effects is a main task for scalable quantum computation. To fight against cavity decay, in typical circuit [3] and cavity[4] QED systems, convectional wisdom is to resort to the so-called large detuning interaction method.Similarly, in trapped thermal ions system, the famous bichromatic excitation scheme [5] couples ions by virtue excitation of phonon mode, also uses the large detuning interaction. Later investigation shows that the logical operation obtained is of the geometric nature [6] and therefore has high fidelity [7].…”