Qubit Protection in Nuclear-Spin Quantum Dot Memories

Abstract

We present a mechanism to protect quantum information stored in an ensemble of nuclear spins in a semiconductor quantum dot. When the dot is charged the nuclei interact with the spin of the excess electron through the hyperfine coupling. If this coupling is made off-resonant, it leads to an energy gap between the collective storage states and all other states. We show that the energy gap protects the quantum memory from local spin-flip and spin-dephasing noise. Effects of nonperfect initial spin polarization and inhomogeneous hyperfine coupling are discussed. DOI: 10.1103/PhysRevLett.103.010502 PACS numbers: 03.67.Pp, 03.65.Yz, 73.21.La, 76.70.Àr An essential ingredient for quantum computation and long-distance quantum communication is a reliable quantum memory. Nuclear spins in semiconductor nanostructures are excellent candidates for this task. With a magneton 3 orders of magnitude weaker than electron spins, they are largely decoupled from their environment, and the hyperfine interaction with electron spins allows one to access ensembles of nuclear spins in a controlled way [1][2][3][4][5][6][7][8][9][10]. In particular, the quantum state of an electron spin can be mapped onto the nuclear spins, giving rise to a longterm memory [3][4][5][6][7]. Nevertheless, memory lifetimes are limited, e.g., by dipole-dipole interactions among the nuclei. In this Letter, we demonstrate that the presence of the electron spin in the quantum dot substantially reduces the decoherence of this collective memory associated with surrounding nuclear spins. The virtual transitions between electronic and nuclear states can be used to produce an energy shift proportional to the number of excitations in the storage spin-wave mode. This isolates the storage states energetically and protects them against nuclear-spin flips and spin diffusion.Consider a quantum dot charged with a single excess electron as indicated in Fig. 1. The electron spinŜ is coupled to the ensemble of underlying nuclear spinsÎ j by the Fermi contact interaction,where A is the average hyperfine interaction constant, A % 90 eV for GaAs, and % j is proportional to the electron density at the position of the jth nucleus, P j % j ¼ 1. For convenience, we introduce the collective operatorŝ A P j % jÎ j . The first term in Eq. (1) yields the Overhauser field, an effective magnetic field for the electron, and also the Knight shift for each nuclei. The flip-flop terms in Eq. (1) As will be shown here, the same can be used to provide a protective energy gap. Fully polarized nuclei.-We start by reconsidering the storage of a qubit in collective nuclear states [3]. In the case when all the nuclear spins are initially polarized in the Àz direction (zero temperature limit), the j#i e and j"i e spin states of the electron are mapped onto the nuclear-spin states j0i j À I; ÀI; . . . ; ÀIi and j1i A  þ j0i / X j % j j ÀI;...;ðÀI þ 1Þ j ;...;ÀIi; (2) respectively.Ĥ JC couples the state j0ij "i e to j1ij #i e with an angular frequency ¼ Að P j % 2 j 2IÞ 1=2 . The detuning between ...

Measurement of the Knight field and local nuclear dipole-dipole field in an InGaAs/GaAs quantum dot ensemble

“…The dynamics of this complex system is only beginning to be understood, but clearly holds the key to achieving long electron spin qubit coherence times for use in applications such as quantum information processing, whilst the Knight field plays a crucial role in novel schemes for the use of QD nuclear spins as a quantum memory [54].…”

Quantum interface between light and nuclear spins in quantum dots

“…In the high-polarization regime 1 − P ≪ 1 a very convenient bosonic description for the nuclear spins becomes available: all excitations out of the fully polarized state and in particular the collective spin operator A + are approximated by bosonic creation operators applied to the N -mode vacuum state 12,13 . Replacing…”

Nuclear spin dynamics in double quantum dots: Multistability, dynamical polarization, criticality, and entanglement

“…In this context, nuclear spins in the surrounding semiconductor host environment have attracted considerable theoretical [13][14][15][16][17][18][19] and experimental [20][21][22][23][24][25] attention, as they have been identified as the main source of electron spin decoherence due to the relatively strong hyperfine (HF) interaction between the electronic spin and N ∼ 10 6 nuclei [5]. However, it has also been noted that the nuclear spin bath itself, with nuclear spin coherence times ranging from hundreds of microseconds to a millisecond [5,26], could be turned into an asset, for example, as a resource for quantum memories or quantum computation [27][28][29][30][31]. Since these applications require yet unachieved control of the nuclear spins, novel ways of understanding and manipulating the dynamics of the nuclei are called for.…”