Nonlinear decoherence in quantum state preparation of a trapped ion

Abstract

We present a nonlinear decoherence model which models decoherence effect caused by various decohereing sources in a quantum system through a nonlinear coupling between the system and its environment, and apply it to investigating decoherence in nonclassical motional states of a single trapped ion. We obtain an exactly analytic solution of the model and find very good agreement with experimental results for the population decay rate of a single trapped ion observed in the NIST experiments by coworkers (D. M. Meekhof, et al., Phys. Rev. Lett. 76, 1796 (1996)). PACS numbers: 32.80. Pj, 42.50.Lc, 03.65.Bz, 05.45.+b In recent years, much progress has been made in preparation, manipulation, and measurement of quantum states of the center-of-mass vibrational motion of a single trapped ion experimentally [1][2][3][4][5][6][7][8] and theoretically [9][10][11][12][13][14][15][16], which are not only of fundamental physical interest but also of practical use for sensitive detection of weak signals [17] and quantum computation in an ion trap [3,9]. In particular, the NIST group [4] has experimentally created and observed nonclassical motional states of a single trapped ion. In the NIST experiments [4], an anti Jaynes-Cummings model (JCM) interaction between the internal and motional states of a trapped ion is realized through stimulated Raman transitions, which couple internal states of the trapped ion to its motional states, when the Lamb-Dicke limit is satisfied and the driving laser fields are tuned to the first blue sideband. Detection of motional states is carried out by observing the evolution characteristics of quantum dynamics of internal levels of the trapped ion under influence of the anti JCM-typed interaction. The NIST experiments revealed the fact that the population of the low atomic state (P ↓ ) evolves according to the following phenomenological expressionwhere p n is the initial probability distribution of motional states of the trapped ion in the Fock representation, g is a coupling constant between the atomic internal and motional states, γ n is a decay rate. The experimentally observed decay rate is of the following formwhere the observed value of ν is ν . = 0.7. A question that naturally arises is: how to explain the above experimentally observed decay rate? It is generally accepted that the appearance of the decay factor γ n in the evolution of internal states is a consequence of decoherence. It is of practical significance to well understand decoherence for preparation of nonclassical states and quantum computation in ion traps. There are various sources of decoherence [1], such as ion vibrational decoherence, ion internal-state decoherence, decoherence caused by non-ideal external fields, and so on. Recently, Schneider and Milburn [18] have investigated decoherence due to laser intensity and phase fluctuations and obtained the power ν in Eq.(2) being ν . = 0.5 instead of the experimentally observed value 0.7. More recently, Murao and Knight [19], using master equation method, have studied decohe...

Decoherence and the nature of system-environment correlations

“…Describing pure decoherence (phase damping), we will assume a standard model [20,21] [9,[22][23][24][25].…”

Amplification of quantum discord between two uncoupled qubits in a common environment by phase decoherence

“…Therefore there is no energy dissipation in this system. Note that this form of coupling has been used to study quantum decoherence in Bose-Einstein condensation and trapped ion by Kuang and coworkers [37]. The renormalization term has the following form…”

Consistent perturbative treatment of the subohmic spin-boson model yielding arbitrarily smallT2/T1decoherence time ratios

“…In principle, an exact solution of the spin-boson model in the same perpendicular coupling case θ = π/2 was also obtained 14 , which however does not lend itself to a description of the effective qubit dynamics because tracing out the bath is still highly nontrivial. Furthermore, in the simple case that the coupling direction and the energy basis direction of the system are parallel (θ = 0), the spin-boson model is also exactly solvable 15,16 .Away from the limiting cases of parallel and perpendicular coupling, θ = 0, π/2, perturbative approaches have been employed 6,7,9,16 . However, as pointed out in 16 , the previous perturbative approaches show a pathological behavior for the subohmic heat bath by predicting the instantaneous loss of phase coherence for any finite coupling η.…”