Enhancing the sensitivity of an atom interferometer to the Heisenberg limit using increased quantum noise

Abstract

In a conventional atomic interferometer employing N atoms, the phase sensitivity is at the standard quantum limit: 1 / N . Under usual spin squeezing, the sensitivity is increased by lowering the quantum noise. It is also possible to increase the sensitivity by leaving the quantum noise unchanged while producing phase amplification. Here we show how to increase the sensitivity, to the Heisenberg limit of 1 / N , while increasing the quantum noise by N and amplifying the phase by a factor of N . Because of the enhancement of the quantum noise and the large phase magnification, the effect of excess noise is highly suppressed. The protocol uses a Schrödinger cat state representing a maximally entangled superposition of two collective states of N atoms. The phase magnification occurs when we use either atomic state detection or collective state detection; however, the robustness against excess noise occurs only when atomic state detection is employed. We show that for one version of the protocol, the signal amplitude is N when N is even, and is vanishingly small when N is odd, for both types of detection. We also show how the protocol can be modified to reverse the nature of the signal for odd versus even values of N . Thus, for a situation where the probability of N being even or odd is equal, the net sensitivity is within a factor of 2 of the Heisenberg limit. Finally, we discuss potential experimental constraints for implementing this scheme via one-axis-twist squeezing employing the cavity feedback scheme, and show that the effects of cavity decay and spontaneous emission are highly suppressed because of the increased quantum noise and the large phase magnification inherent to the protocol. As a result, we find that the maximum improvement in sensitivity can be close to the ideal limit for as many as 10 million atoms.

Using interaction-based readouts to approach the ultimate limit of detection-noise robustness for quantum-enhanced metrology in collective spin systems

“…The reason why there is no need for the extra application of U flip is because the state U † 1 |ψ φ already yields a probability distribution identical to P opt , and is unchanged by application of U flip . The outstanding performance of the echo IBR for this state was first reported in 60 and subsequently in, 61,65 but it was not known that this is the maximum achievable sensitivity § . † For odd N we require an additional rotation: an equal superposition cat is generated by e i π 2Ĵ y e i π 2Ĵ 2 y |m .…”

Improving cold-atom sensors with quantum entanglement: Prospects and challenges

“…51,229,230 Methods of alleviating these requirements and improving robustness by subsequently undoing the entanglement generation after the phase-encoding (so-called "interaction-based readouts") is an active field of research. 133,150,228,[231][232][233][234][235][236][237][238][239][240] Despite their fragility, under the right circumstances entangled non-Gaussian states could prove beneficial even in the presence of noise. An example is when a protocol is limited not by the atomic decoherence time, but rather by the coherence time of the probing laser.…”

Sensitivity of a Point-Source-Interferometry-Based Inertial Measurement Unit Employing Large Momentum Transfer and Launched Atoms

“…A one-axis PSI can be used for measuring acceleration along the primary axis and two components of rotation along the axes orthogonal to the primary axis. In a conventional atomic interferometer, the signal is determined by measuring the total population of the atoms in a particular internal quantum state, and there exists a well-developed method for the sensitivity limit analysis for such a detection scheme [12,13]. However, for a PSI, the information about the acceleration and the rate of rotation is distributed spatially over the whole atomic cloud.…”