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Effects of that drift become apparent for instance in Fig. The drift may be caused by magnetic field variations or changes of the hyperfine coupling. However, because is much smaller than T c the latter effect is even smaller.
Instead of performing a phase estimation-like sequence as displayed in Fig. In that case one performs the first phase accumulation only on the sensor utilizing purely local gates Subsequently, the phase is swapped and kept on the memory during T c.
It is retrieved before the second sensing time via another SWAP-gate. Finally, the memory is correlated with the phase of the sensor. However, this is more costly in terms of RF pulses and interference. Hence, it is less time and energy efficient. The latter fact is vital, since control of nuclear spins takes longer even at much higher driving field strengths due to their much smaller magnetic moment. The SWAP-gate based approach requires significantly more resources.
Interestingly, our novel sensing sequence requires a comparable quantity of gates, time and energy to the conventional sequence see Fig. In addition, the storage and retrieval pulses on the memory act during the correlation time and therefore might interfere with what is going on during this time for example, dynamics of interest or control of other spins. Comparing conventional and enhanced correlation spectroscopy methods, we find that despite almost equal duration of both sequences, the enhanced method is slightly more complex because C n ROT e -gates instead of local gates on the sensor are involved.
The applied optimal control C n ROT e -gates seem to cope well with the increased complexity.
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In fact, the signal contrast shows indeed the expected factor of two compared with the conventional method see Figs 2a,b and 8. Analysis of fits to Fig.
The initial signal contrast A 0 that is, twice the initial amplitude of the decaying oscillation is plotted for increasing sensing time and for enhanced and conventional measurement sequence top and bottom, respectively. The horizontal lines are weighted averages of the signal contrast for both cases and their values are given. Please note, that the error bars give standard errors taken from the used least square fit. Variable entanglement. Variable entanglement between sensor and memory is created after initializing the system into. The latter part is dependent on the memory state and therefore creates entanglement.
The -gate is designed such that for no phase accumulation during the sensor state is finally regardless of the memory state. As illustrated in Fig. For the given initial state we can calculate the negativity of the entangled state, where is an applicable entanglement measure that ranges from for no entanglement to for a Bell state 24 , For the present case of variable entanglement we have to mind the hyperfine interaction which constitutes controlled z -rotations on the sensor spin and leads to additional quantum correlations during and T c.
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For our experiments with variable entanglement we choose the latter time intervals such that no additional correlations are created. Then we do the analogous experiments to those presented in Fig. We fit the oscillations and from their amplitudes we deduce the amount of stored information see Fig. In addition to the experiment, we calculate the theoretically expected result for perfect sensor, memory, quantum gates and readout.
For each degree of entanglement , we propagate the initial state through the entire sequence. We have fit equation 16 to the measured signal contrasts for variable entanglement by scaling its function values see Fig. The data supporting the findings of this study are available from the corresponding author on request. How to cite this article: Zaiser, S. Enhancing quantum sensing sensitivity by a quantum memory.
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