Enhancing quantum sensing sensitivity by a quantum memory

Introduction

Precision sensing using quantum states usually relies on accurate measurements of their quantum phase. However, numerous susceptibilities to environmental noise make quantum states fragile resulting in limited sensitivity. Therefore, the acquisition of a large phase is a central challenge1,2,3,4,5. Typically, two strategies are used to enhance quantum sensing: one way is multi-particle entanglement of sensing qubits which results in rapid phase accumulation, but often is counterbalanced by faster dephasing6,7,8. Entanglement, however, pays off, if fluctuations of the quantity to be measured have a shorter correlation time than the single sensor coherence time. A long-lived memory is another way which is advantageous when the quantity to be measured has a longer correlation time than the sensor’s coherence time9,10,11,12. The quantum memory approach is particularly suited in hybrid sensor systems where the sensing qubit strongly interacts with the quantity to be measured while the storage qubit is well isolated from environmental influences except for its coupling to the sensor. Typically, highest sensitivity is reached when the available coherence time of the sensing qubit is most effectively used13,14,15. Further enhancement is gained if the quantum state of the sensing qubit is at least partially stored for a later feedback, and thereby exploiting the observable’s longer correlation time9,10,12.

Here, we utilize a quantum memory for full storage of the sensor’s quantum state leading to enhanced sensitivity. We demonstrate that entanglement of quantum memory and sensing qubit during the phase accumulation process makes efficient use of the resources at hand. The enhanced sensing time due to use of the quantum memory improves spectral resolution. A further benefit of our phase estimation-type16protocol are non-local gate operations between quantum memory and, for example, a sample spin.

We exploit the benefits of the quantum memory by a measurement protocol based on the correlating two subsequent phase estimation steps. If the correlation time of the measured quantity (for example, a magnetic field) is longer than the coherence time of the sensor, this coherence time limits the measurement resolution and makes recording of the dynamics challenging. To recover dynamics and increase spectral resolution, subsequently measured quantities S can be correlated (that is, ). However, because the measurement exhibits a limited visibility A<1 of the measurement signal S, the visibility of a correlation measurement decreases as ∝A2. One solution are classical correlation measurements9,10,17,18,19,20,21,22,23, where a long-lived memory stores information. If memory and sensing qubit are not entangled, typically half of the signal amplitude A is lost. Full SWAP-gates between quantum sensor and quantum memory on the other hand require excessive operation on the quantum register, which leads to a reduced overall fidelity. Here, we retain the full measurement contrast A by entangling sensor and memory qubit. Furthermore, we show that storing the full quantum state not only allows for improved detection of weakly coupled qubits, but also enables coherent interaction and non-local gates between memory and distinct weakly coupled qubits.

Results

Entangling sensor and memory qubit

We use the electron spin of a nitrogen-vacancy (NV) centre in diamond and the associated 14N nuclear spin14 to build a hybrid quantum sensor-memory pair (see Fig. 1a,b). While the electron spin serves as a magnetic field sensor, the nuclear spin acts as a quantum memory due to its much weaker coupling to the environment. The coherence of the memory decays slightly slower than the electron spin lattice relaxation time14, T1,sensor=(4.94±0.16) ms, whereas the sensor coherence decays more than one order of magnitude faster in a spin echo measurement,T2,sensor=(395±5) μs (see Fig. 1d). Hence, we can gain up to one order of magnitude in frequency and equivalently field resolution by using the nuclear spin as memory. To demonstrate the role of entanglement between the sensor and the quantum memory we gradually increase entanglement between them and measure the resulting sensing accuracy. We further test the novel scheme for entangling the memory qubit and a proximal 13C nuclear spin. We use the tiny magnetic field of weakly coupled 13C nuclear spins as measurement quantity with extremely long correlation time.

Figure 1: System parameters and measurement sequence.

(a) Structure of an NV defect centre in diamond45. Two adjacent lattice sites are occupied by a nitrogen atom and a vacancy. (b) Energy-level structure of NV electron spin e (S=1) and hyperfine coupled 14N nuclear spin n (I=1). Four out of nine spin states form the two-qubit basis-states . They are eigenstates to electron spin operator Sz and nuclear spin operator Iz with respective magnetic quantum numbers mS and mI (see the ‘Methods’ section). Addressed spin transitions are marked with vertical red lines. (c) Quantum wire diagrams for quantum phase correlation measurements. Grey indicates general idea. Two quantum gates  controlled by the memory qubit state represent our phase estimation steps with duration τ at times t (that is, with separation Tc). Filled (open) circles indicate  controlled gates. If both quantum gates are equal, the total phase on the memory is zero. Purple indicates the enhanced sequence with full entanglement of sensor and memory. Experimental implementation using controlled spin rotations (for example, π/2-pulses and π-pulses) of the sensor (memory) controlled by the memory (sensor) and free evolution times  and Tc. Orange indicates sequences with variable degree of entanglement between sensor and memory realized via the η- and -gate (see the ‘Methods’ section). (d) Measurements of the electron spin’s T1 and T2 time via measurement of the spin state population decay and a spin echo measurement (squares and circles). The inset shows the quantum wire diagrams of the respective measurement sequences. The signal is the probability of detecting the memory spin state  and the contrast is the difference of two signals with the final π-pulse on the memory controlled by the  and  state of the sensor.