Supersensitive quantum sensor based on criticality in an antiferromagnetic spinor condensate

Abstract

We consider an antiferromagnetic Bose-Einstein condensate in a traverse magnetic field with a fixed macroscopic magnetization. The system exhibits two different critical behaviors corresponding to transitions from polar to broken-axisymmetry and from antiferromagnetic to broken-axisymmetry phases depending on the value of magnetization. We exploit both types of system criticality as a resource in the precise estimation of control parameter value. We quantify the achievable precision by the quantum Fisher information. We demonstrate the super-sub-shot noise sensitivity and show that the precision scales with the number of atoms up to N 4 around critically. In addition, we study the precision based on the error-propagation formula providing the simple-to-measure signal which coincides its scaling with the quantum Fisher information. Finally, we take into account the effect of non-zero temperature and show that the sub-shot noise sensitivity in the estimation of the control parameter is achievable in the low-temperature limit.

Adiabatic critical quantum metrology cannot reach the Heisenberg limit even when shortcuts to adiabaticity are applied

“…of a critical system, optimal regular quantum metrology is always superior to critical quantum metrology given the same amount of time resources. We confirmed that previous reports [20,69] on beating the HL in critical quantum metrology are a consequence of neglecting the time required to prepare a critical state [23]. We have also shown that shortcuts to adiabaticity, specifically counter-diabatic driving, cannot be used to reach or overcome the HL, although they allow the critical ground state to be prepared in arbitrary short times.…”

“…Critical quantum metrology will also be advantageous if the initial state of the system of interest is already (close to) the critical ground state and therefore the associated time resources for preparing a critical state can be neglected which however, is not often the case in real experimental setups. The oft-cited super-Heisenberg scaling in critical quantum metrology achievable in critical quantum metrology I ∆ ∼ N >2 [69] derives from the fact that the QFI is calculated without considering the adiabatic protocol time. When this time duration is included [20,23], the apparent super-Heisenberg scaling vanishes and the sensitivity is limited by the HL I ∆ < N 2 T 2 .…”

Quantum phases transition revealed by the exceptional point in Hopfield-Bogoliubov matrix

“…Quantum phase transitions are playing an increasingly important role in many fields, such as, quantum metrology [1][2][3][4][5][6][7][8][9][10][11][12], which involves using quantum resources to improve measurement precision. The superradiant phase (SP) transition is one of the most important quantum phase transition, which was proposed in the Dicke model for the first time in 1970's [13].…”

Critical parametric quantum sensing

“…A promising approach to quantum sensing exploits quantum fluctuations in the proximity of the criticality to improve the measurement precision. Despite a critical slowing down at the phase transition, theoretical analyses of many-body systems [3][4][5][6][7][8][9][10][11][12][13][14][15][16] show that critical quantum sensors can achieve the optimal scaling of precision [17], both in the number of probes and in the measurement time [9]. Furthermore, it has been shown [18] that finitecomponent phase transitions [19][20][21][22][23]-where the thermodynamic limit is replaced by a scaling of the system parameters [24][25][26][27][28]-can also be applied in sensing protocols.…”