Planar quantum squeezing and atom interferometry

Abstract

Reduction of quantum noise in one spin component is a significant tool for enhancing the sensitivities of interferometers and atomic clocks. It has been recently implemented for ultra-cold atomic Bose-Einstein condensate (BEC) interferometer. This type of quantum noise reduction reduces the measurement noise near some predetermined phase. However, if the phase is completely unknown prior to measurement, then it is not known which phase quadrature should be in a squeezed state. We introduce a novel planar squeezing uncertainty relation for spin variance in a plane, and analyze how to obtain such a planar quantum squeezed (PQS) state by using a double-well single component BEC, through the use of local nonlinear S-wave scattering interaction between trapped atoms. Here, we consider the PQS that is generated by using two hyperfine states in a two components BEC system, which is useful for quantum metrology. By comparison with the case of two spatial wells, the Hamiltonian parameters can be controlled in a more efficient way. The spin component can be measured by detecting the occupation number difference between the two internal modes, while one needs to observe a spatial interference pattern in the double well BEC case. This is the major difference between the internal and external cases. Another difference is that one can use the Rabi frequency Ω instead of the Josephson parameters to switch the Hamiltonian parameters through using a diabatic technique. Therefore the coupling could be switched off or on to study the different evolutions. PQS simultaneously reduces the quantum noises of two orthogonal spin projections below the standard quantum limit, while increases the noise in the third dimension. This allows the improvement in phase measurement at any phase-angle. PQS states that reductions of fluctuations everywhere in a plane have potential utility in "one-shot" phase measurement, where iterative or repeated measurement strategies cannot be utilized. The improved interferometric phase measurements and planar uncertainty relations are useful for detecting the entanglement in mesoscopic system between two distinguished modes regardless of the third component.

Tunable two-axis spin model and spin squeezing in two cavities

“…The ultrahigh-finesse cavities interacting with two-level particles (such as atoms, nitrogen vacancy centers, superconducting qubits, etc) are also powerful platforms to produce effective spin squeezing, since the photon of cavity mode can induce nonlinear spin-spin interaction and thus generate the required one-axis twisting Hamiltonian. [20][21][22][23][24][25][26][27][28][29][30] Recently, multi-mode cavities [31] have attracted much attention both experimentally and theoretically. [32][33][34][35][36][37] On one hand, these setups can be used to explore novel physics, such as the spin-orbit-induced anomalous Hall effect, [38,39] the crystallization and frustration, [40,41] the spin glass, [42][43][44][45] and the gapless Nambu-Goldstone-type mode without rotating-wave approximation.…”