Nuclear spin state narrowing via gate-controlled Rabi oscillations in a double quantum dot

Abstract

We study spin dynamics for two electrons confined to a double quantum dot under the influence of an oscillating exchange interaction. This leads to driven Rabi oscillations between the |↑↓ -state and the |↓↑ -state of the two-electron system. The width of the Rabi resonance is proportional to the amplitude of the oscillating exchange. A measurement of the Rabi resonance allows one to narrow the distribution of nuclear spin states and thereby to prolong the spin decoherence time. Further, we study decoherence of the two-electron states due to the hyperfine interaction and give requirements on the parameters of the system in order to initialize in the |↑↓ -state and to perform a √ SWAP operation with unit fidelity.

Maximizing the purity of a qubit evolving in an anisotropic environment

“…However, for each bath initial state, it will be important to justify the Gaussian approximation used to derive Eq. (22). This approximation is very good for an uncorrelated thermal bath or a sufficiently random 'narrowed' state, 71 but may break down for pure initial conditions with strong (classical or quantum) correlations.…”

“…II to the problem of Hahn echo, using the leading-order Magnus expansion and Gaussian approximation to obtain the approximate generator L(2τ ) L 0 (2τ ) given in Eq. (22). See Refs.…”

“…This topic has become especially interesting in the context of spin-bath dynamics. [17][18][19][20] For slowly-evolving nuclear-spin baths, it is indeed possible to approach pure-state initial conditions through algorithmic cooling [9][10][11] or direct measurement of the bath state, 13,[21][22][23][24][25] so studying the purity for these systems is especially important from both a practical and a fundamental point of view.…”

Quantum Computing with Spins in Solids

“…The √ swap operation has now been successfully implemented in experiments involving two electrons confined to two neighboring quantum dots (as in Figure 1) (Petta et al 2005a. Errors during the √ swap operation have been investigated due to nonadiabatic transitions to higher orbital states (Schliemann et al 2001, Requist et al 2005, spin-orbit-interaction (Bonesteel et al 2001, Stepanenko et al 2003, and hyperfine coupling to surrounding nuclear spins (Petta et al 2005a, Klauser et al 2005, Taylor et al 2006. The isotropic form of the exchange interaction given in Equation (1) is not always valid.…”

“…This work has shown that, while the longitudinal spin decay is bounded by ∼ 1/p 2 N , due to the quantum nature of the nuclear field, the transverse components of spin will decay to zero in a time t c ≈ 5 ns/ 1 − p 2 (without ensemble averaging and without making a mean-field ansatz), unless an electron spin echo sequence is performed or the nuclei are prepared in an eigenstate of the operator h z 0 through measurement (Coish and Loss 2004). There are several recent suggestions for methods that could be used to measure the operator h z 0 , Klauser et al 2005, Stepanenko et al 2005) in order to extend electron spin decoherence. Once the nuclear spin system is forced into an eigenstate of h z 0 , the lowest-order corrections for large magnetic field still show incomplete decay for the transverse spin (Coish and Loss 2004), suggesting that dynamics induced by the nuclear dipolar interaction may limit spin coherence in this regime (de Sousa and Das Sarma 2003), although higher-order corrections have been reported to lead to complete decay (Deng and Hu 2005), even when the nuclear spin system is static.…”