Extreme Phase-Amplification under Direct Detection of Atomic States for Heisenberg Limited Sensitivity in an Atomic Interferometer Employing Schroedinger Cat States
We show that for an N-particle atom interferometer, an N-fold reduction in fringe-width due to phase amplification can be achieved via direct detection of atomic states, employing Schroedinger Cat states, yielding Heisenberg limited sensitivity.
In a conventional atomic interferometer employing N atoms, the phase sensitivity is at the standard quantum limit: 1/N. Using spin-squeezing, the sensitivity can be increased, either by lowering the quantum noise or via phase amplification, or a combination thereof. Here, we show how to increase the sensitivity, to the Heisenberg limit of 1/N, while increasing the quantum noise by N, thereby suppressing by the same factor the effect of excess noise. The protocol uses a Schrodinger Cat state representing a superposition of two collective states of N atoms, behaving as a single entity with an N-fold increase in Compton frequency. The resulting N-fold phase magnification is revealed by using atomic state detection instead of collective state detection. We also show how to realize an atomic clock based on such a Schrodinger Cat state, with an N-fold increase in the effective transition frequency. We discuss potential experimental constraints for implementing this scheme, using one axis twist squeezing employing the cavity feedback scheme, and show that the effects of cavity decay and spontaneous emission are highly suppressed. We find that the maximum improvement in sensitivity can be close to the ideal limit, for as many as ten million atoms.
In a conventional atomic interferometer employing N atoms, the phase sensitivity is at the standard quantum limit: 1/N. Using spin-squeezing, the sensitivity can be increased, either by lowering the quantum noise or via phase amplification, or a combination thereof. Here, we show how to increase the sensitivity, to the Heisenberg limit of 1/N, while increasing the quantum noise by N, thereby suppressing by the same factor the effect of excess noise. The protocol uses a Schrodinger Cat state representing a superposition of two collective states of N atoms, behaving as a single entity with an N-fold increase in Compton frequency. The resulting N-fold phase magnification is revealed by using atomic state detection instead of collective state detection. We also show how to realize an atomic clock based on such a Schrodinger Cat state, with an N-fold increase in the effective transition frequency. We discuss potential experimental constraints for implementing this scheme, using one axis twist squeezing employing the cavity feedback scheme, and show that the effects of cavity decay and spontaneous emission are highly suppressed. We find that the maximum improvement in sensitivity can be close to the ideal limit, for as many as ten million atoms.
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.