Thresholded quantum sensing with a frustrated Kitaev trimer

We investigate the response of a Ramsey interferometric quantum sensor based on a frustrated, three-spin system (a Kitaev trimer) to a classical time-dependent field (signal). The system eigenspectrum is symmetric about a critical point, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mo>|</a:mo> <a:mi mathvariant="bold-italic">b</a:mi> <a:mo>|</a:mo> <a:mo>=</a:mo> <a:mn>0</a:mn> </a:mrow> </a:math> , with four of the spectral components varying approximately linearly with the magnetic field and four exhibiting a nonlinear dependence. Under the adiabatic approximation and for appropriate initial states, we show that the sensor's response to a zero-mean signal is such that below a threshold, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mrow> <c:mo>|</c:mo> <c:mi mathvariant="bold-italic">b</c:mi> <c:mo>|</c:mo> <c:mo>&lt;</c:mo> </c:mrow> <c:msub> <c:mi>b</c:mi> <c:mi>th</c:mi> </c:msub> </c:mrow> </c:math> , the sensor does not respond to the signal, whereas above the threshold, the sensor acts as a detector that the signal has occurred. This thresholded response is approximately omnidirectional. Moreover, when deployed in an entangled multisensor configuration, the sensor achieves sensitivity at the Heisenberg limit. Such detectors could be useful both as stand-alone units for signal detection above a noise threshold and in two- or three-dimensional arrays, analogous to a quantum bubble chamber, for applications such as particle track detection and long-baseline telescopy.