We consider the spin echo decay of a nitrogen-vacancy center spin qubit, based on
m=0 and
m=1 levels of the
S=1 ground state spin manifold of the center, in presence of finite dynamic nuclear polarization of the nuclear environment. We show that the signal acquires a nontrivially time-dependent phase shift in presence of such polarization. In Gaussian approximation to calculation of dephasing this phase shift is absent when the NV center is prepared in a superposition of
m=1 and
m=−1 states, i.e. when the qubit couples to the spin environment in a way analogous to that of spin-
1/2. For nuclear environment devoid of spins strongly coupled to the qubit, the phase shift can be quite well described in Gaussian approximation, which makes it clear that it is related to a linear response function of the environment affected by an evolving qubit. Consequently, its observation signifies the presence of back-action of the qubit on the environment, and it thus excludes the possibility of physically well-motivated treatment of environment as a source of external classical noise affecting the qubit. Furthermore, when exact coherence dynamics is well described by weak coupling approximation, for qubit based on
m=0 and
m=1 levels observation of dependence of modulus of echo signal on nuclear polarization signifies non-Gaussian character of environmental influence. The same conclusion follows from observation of nonzero phase shift of spin echo signal of a qubit based on
m=±1 levels.
Abstract Nuclear magnetic resonance (NMR) of single spins have recently been detected by quantum sensors. However, the spectral resolution has been limited by the sensor’s relaxation to a few kHz at room temperature. This can be improved by using quantum memories, at the expense of sensitivity. In contrast, classical signals can be measured with exceptional spectral resolution by using continuous measurement techniques, without compromising sensitivity. When applied to single-spin NMR, it is critical to overcome the impact of back action inherent of quantum measurement. Here we report sequential weak measurements on a single 13C nuclear spin. The back-action causes the spin to undergo a quantum dynamics phase transition from coherent trapping to coherent oscillation. Single-spin NMR at room-temperature with a spectral resolution of 3.8 Hz is achieved. These results enable the use of measurement-correlation schemes for the detection of very weakly coupled single spins.
Decoherence of a quantum system arising from its interaction with an environment is a key concept for understanding the transition between the quantum and classical world as well as performance limitations in quantum technology applications. The effects of large, weakly coupled environments are often described as a classical, fluctuating field whose dynamics is unaffected by the qubit, whereas a fully quantum description still implies some backaction from the qubit on the environment. Here we show direct experimental evidence for such a backaction for an electron-spin qubit in a GaAs quantum dot coupled to a mesoscopic environment of order 10^{6} nuclear spins. By means of a correlation measurement technique, we detect the backaction of a single qubit-environment interaction whose duration is comparable to the qubit's coherence time, even in such a large system. We repeatedly let the qubit interact with the spin bath and measure its state. Between such cycles, the qubit is reinitialized to different states. The correlations of the measurement outcomes are strongly affected by the intermediate qubit state, which reveals the action of a single electron spin on the nuclear spins.