High-Density Quantum Sensing with Dissipative First Order Transitions

The sensing of external fields using quantum systems is a prime example of an emergent quantum technology. Generically, the sensitivity of a quantum sensor consisting of $N$ independent particles is proportional to $\sqrt{N}$. However, interactions invariably occurring at high densities lead to a breakdown of the assumption of independence between the particles, posing a severe challenge for quantum sensors operating at the nanoscale. Here, we show that interactions in quantum sensors can be transformed from a nuisance into an advantage when strong interactions trigger a dissipative phase transition in an open quantum system. We demonstrate this behavior by analyzing dissipative quantum sensors based upon nitrogen-vacancy defect centers in diamond. Using both a variational method and a numerical simulation of the master equation describing the open quantum many-body system, we establish the existence of a dissipative first order transition that can be used for quantum sensing. We investigate the properties of this phase transition for two- and three-dimensional setups, demonstrating that the transition can be observed using current experimental technology. Finally, we show that quantum sensors based on dissipative phase transitions are particularly robust against imperfections such as disorder or decoherence, with the sensitivity of the sensor not being limited by the $T_2$ coherence time of the device. Our results can readily be applied to other applications in quantum sensing and quantum metrology where interactions are currently a limiting factor.

Figure 1

Setup of the system for dissipative quantum sensing. (a) Many-body system of nitrogen-vacancy centers in diamond showing individual carbon atoms (gray) and nitrogen impurities (blue) accompanied by a vacancy site (white). The electronic ground state is a triplet state that is split by an external bias field. (b) Sketch of the dimensionless magnetization of the system across a first order phase transition. The response of the system strongly increases for larger system sizes. At the transition, the derivative of the magnetization is proportional to $\sqrt{N}$. The inset shows the sensing protocol consisting of NV initialization, dissipative many-body dynamics, and a readout of the NV spin state.

Figure 2

Variational solution for the steady state magnetization showing a first order phase transition. The phase transition can be triggered by varying either the Rabi frequency $\mathrm{\Omega }$ or the external magnetic field (inset) ($V=2\pi \times 400\mathrm{kHz}$, $\gamma =1\mathrm{MHz}$).

Figure 3

Averaged results from 1000 wave-function Monte Carlo trajectories showing the steady state susceptibility $\chi$ for $3\times 3$ and $4\times 4$ geometries. The solid lines are fits to a Weibull distribution.

Figure 4

Finite size scaling of the peak of the reduced susceptibility $\chi /\tilde{\chi }$. The collapse of the data onto a single line in the logarithmic plot shows that the susceptibility diverges with the system size $N$. The solid line is an algebraic fit to the data.

Figure 5

Variational solution for the magnetization of the central layer in a three-dimensional system. The first order transition is replaced by a smooth crossover. Using a magnetic field gradient (inset), the phase transition can be restored.

Figure 6

Consequences of additional decoherence channels for different $T_2$ times. The first order transition is particularly robust to these additional decoherence processes, even when their associated rates become larger than the strength of the dipole-dipole interaction between the NV centers. Only for very short $T_2$ times is the phase transition replaced by a smooth crossover.