Quantum Coherence Enhancement In A Spinor Bose-Einstein Condensate

Quantum precision measurement focus on using quantum system,quantum proper-ties,or quantum control to perform a high precision measurement of a physical quantity.It plays a crucial role in fundamental science and engineering.Spinor Bose-Einstein con-densate(BEC)has a potential for high precision measurement of magnetic field with its long coherence time and high controllability and fine-tuning in practical experiments Several metrology useful quantum state including squeezed spin state,Dicke state and many body singlet state can be realized in spinor BEC system.However,in practical experiments,from the preparation and manipulation of a quantum state to the preci-sion measurement using a quantum state,it is inevitable be affected by environmental noise.To suppress the noise effect of stray magnetic fields,we employ a continuous driving protocol,rotary echo,to enhance the spin coherence of a spin-1 Bose-Einstein conden-sate.Our analytical and numerical results show that the effect of the stray magnetic fields are maximally suppressed,if the condition h?=m?,m=1,2,3,…is met with h the pulse amplitude and pulse width.Under such magic condition,the coherent and the squeezed spin states are preserved for a significantly long time,compared to the free induction decay time,In particular,both the spin average and the spin squeezing,including the direction and the amplitude,are simultaneously fixed for a squeezed spin state.Dynamical decoupling techniques are effective for extending coherence time in spin systems,and thus to improve the the coherent evolution time of the system for precision measurements.For a magnetometer,dynamical decoupling is only suited to the mea-surement of a alternate-current magnetic field.Because dynamical sequence invert the system periodically,and thus cancels the accumulated phases for both noise field and static magnetic fields.Therefore,we propose the phase relay method to revive the mod-ulated phase due to the interaction between the spin system and static magnetic field to a monotonically increasing form.Thus,we realize the measurement of a static magnetic field.Our numerical verification is implement specifically on 87Rb spin-1 Bose-Einstein condensate under Balanced-Unidd scheme.For a coherent spin state of 10000 atoms in the presence of noise with intensity of 0.1mG,we achieve the measurement of a static magnetic field of?0.16mG and obtain a magnetic field sensitivity of 0.36pT/(?)within 200ms.Meanwhile,a magnetic field sensitivity of 64fT/(?)is attained for a maximal squeezed spin state under the same condition.And the static field measured with squeezed spin state is of 0.0016mG.It is worth to emphasis that magnetic field sensitivity achieve with coherent spin state is the standard quantum limit(SQL)for 1000 spinl atoms,while the magnetic field sensitivity for squeezed spin state is beyond the SQL.In our perspective,the pulses are treated as artificial imposed coherent strong noise to the system whose effect is inverting the spin and canceling the consequence of environmental noise.Therefore,we can recover the modulated phase by doing the inverse operation of pulses.The phase relay method is universal,hence can be utilized to other measurement scheme of DC fields.