Singlet-triplet decoherence due to nuclear spins in a double quantum dot

Abstract

We have evaluated hyperfine-induced electron spin dynamics for two electrons confined to a double quantum dot. Our quantum solution accounts for decay of a singlet-triplet correlator even in the presence of a fully static nuclear spin system, with no ensemble averaging over initial conditions. In contrast to an earlier semiclassical calculation, which neglects the exchange interaction, we find that the singlet-triplet correlator shows a long-time saturation value that differs from 1/2, even in the presence of a strong magnetic field. Furthermore, we find that the form of the long-time decay undergoes a transition from a rapid Gaussian to a slow power law ($\sim 1/t^{3/2}$) when the exchange interaction becomes nonzero and the singlet-triplet correlator acquires a phase shift given by a universal (parameter independent) value of $3\pi/4$ at long times. The oscillation frequency and time-dependent phase shift of the singlet-triplet correlator can be used to perform a precision measurement of the exchange interaction and Overhauser field fluctuations in an experimentally accessible system. We also address the effect of orbital dephasing on singlet-triplet decoherence, and find that there is an optimal operating point where orbital dephasing becomes negligible.Comment: 12 pages, 4 figure

Orbital and spin relaxation in single and coupled quantum dots

“…At low magnetic fields ͑say, tens of gauss͒, the relaxation proceeds via hyperfine coupling of the electron spin with the lattice or impurity nuclei. [4][5][6] On the other hand, at higher fields ͑Teslas͒ the relaxation is due to phonon-induced spin-flip transitions. [7][8][9][10][11][12][13][14][15][16][17][18][19] These are allowed due to the presence of spin-orbit coupling.…”

Maximizing the purity of a qubit evolving in an anisotropic environment

“…(b) Bloch sphere for a singlettriplet (S-T0) qubit subject to a fluctuating nuclear difference field δhz and exchange coupling J with fluctuations δω(t) due to charge noise. 38 All results for the S-T0 model follow directly from the hole-spin model with the replacements hz → 2δhz, γH B → J, γj → 0.…”

“…1, the model presented here for heavy-hole spin dynamics and decoherence can be mapped exactly onto a well-studied model of singlettriplet decoherence. 38 In particular, the heavy-hole spin-S z eigenstates |⇑ and |⇓ can be associated with twoelectron states |↑↓ and |↓↑ for two electron spins in a double quantum dot, making up the singlet |S and triplet |T 0 states:…”

“…[33][34][35][36][37] Heavy-hole spins can indeed approach the extreme-anisotropic limit of a pure Ising-like coupling to nuclear spins. 33 Finally, singlettriplet (S-T 0 ) qubits, describing two electrons in a double quantum dot, are described by precisely the same anisotropic decoherence model 38 as a heavy-hole spin qubit (see Fig. 1).…”

Two-electron dephasing in single Si and GaAs quantum dots

“…In GaAs, the single-spin decoherence time T 2 has been measured to be 1 ns for charge qubit 19,20 , while T 2 for single-spin qubits has been measured to be greater than 100 µs. 21 In the singlet-triplet qubit, when there is a finite exchange-induced energy splitting between the singlet and triplet states, the dominant sources of decoherence have been found to be charge noise [22][23][24] and electronphonon coupling. 25 Much of the physics of the hybrid qubit is similar to that of the singlet-triplet qubit, with the main differences in the decoherence properties arising because one of the dots contains two electrons.…”