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Quantum metrology fundamentally relies upon the efficient management of quantum uncertainties. We show that, under equilibrium conditions, the management of quantum noise becomes extremely flexible around the quantum critical point of a quantum many-body system: this is due to the critical divergence of quantum fluctuations of the order parameter, which, via Heisenbergs inequalities, may lead to the critical suppression of the fluctuations in conjugate observables. Taking the quantum Ising model as the paradigmatic incarnation of quantum phase transitions, we show that it exhibits quantum critical squeezing of one spin component, providing a scaling for the precision of interferometric parameter estimation which, in dimensions $d geq 2$, lies in between the standard quantum limit and the Heisenberg limit. Quantum critical squeezing saturates the maximum metrological gain allowed by the quantum Fisher information in $d=infty$ (or with infinite-range interactions) at all temperatures, and it approaches closely the bound in a broad range of temperatures in $d=2$ and 3. This demonstrates the immediate metrological potential of equilibrium many-body states close to quantum criticality, which are accessible emph{e.g.} to atomic quantum simulators via elementary adiabatic protocols.
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Including collisional decoherence explicitly, phase sensitivity for estimating effective scattering strength $chi$ of a two-component Bose-Einstein condensate is derived analytically. With a measurement of spin operator $hat{J}_{x}$, we find that the optimal sensitivity depends on initial coherent spin state. It degrades by a factor of $(2gamma)^{1/3}$ below super-Heisenberg limit $propto 1/N^{3/2}$ for particle number $N$ and the dephasing rate $1<!<gamma<N^{3/4}$. With a $hat{J}_y$ measurement, our analytical results confirm that the phase $phi=chi tsim 0$ can be detected at the limit even in the presence of the dephasing.
We propose a scheme to realize high-precision quantum interferometry with entangled non-Gaussian states by driving the system through quantum phase transitions. The beam splitting, in which an initial non-degenerate groundstate evolves into a highly entangled state, is achieved by adiabatically driving the system from a non-degenerate regime to a degenerate one. Inversely, the beam recombination, in which the output state after interrogation becomes gradually disentangled, is accomplished by adiabatically driving the system from the degenerate regime to the non-degenerate one. The phase shift, which is accumulated in the interrogation process, can then be easily inferred via population measurement. We apply our scheme to Bose condensed atoms and trapped ions, and find that Heisenberg-limited precision scalings can be approached. Our proposed scheme does not require single-particle resolved detection and is within the reach of current experiment techniques.
Physical systems close to a quantum phase transition exhibit a divergent susceptibility, suggesting that an arbitrarily-high precision may be achieved by exploiting quantum critical systems as probes to estimate a physical parameter. However, such an improvement in sensitivity is counterbalanced by the closing of the energy gap, which implies a critical slowing down and an inevitable growth of the protocol duration. Here, we design different metrological protocols that make use of the superradiant phase transition of the quantum Rabi model, a finite-component system composed of a single two-level atom interacting with a single bosonic mode. We show that, in spite of the critical slowing down, critical quantum optical systems can lead to a quantum-enhanced time-scaling of the quantum Fisher information, and so of the measurement sensitivity.
The Lipkin-Meshkov-Glick (LMG) model describes critical systems with interaction beyond the first-neighbor approximation. Here we address the characterization of LMG systems, i.e. the estimation of anisotropy, and show how criticality may be exploited to improve precision. In particular, we provide exact results for the Quantum Fisher Information of small-size LMG chains made of $N=2, 3$ and $4$ lattice sites and analyze the same quantity in the thermodynamical limit by means of a zero-th order approximation of the system Hamiltonian. We then show that the ultimate bounds to precision may be achieved by tuning the external field and by measuring the total magnetization of the system. We also address the use of LMG systems as quantum thermometers and show that: i) precision is governed by the gap between the lowest energy levels of the systems, ii) field-dependent level crossing provides a resource to extend the operating range of the quantum thermometer.
The diverging responses to parameter variations of systems at quantum critical points motivate schemes of quantum metrology that feature sub-Heisenberg scaling of the sensitivity with the system size (e.g., the number of particles). This sensitivity enhancement is fundamentally rooted in the formation of Schrodinger cat states, or macroscopic superposition states at the quantum critical points. The cat states, however, are fragile to decoherence caused by local noises on individual particles or coupling to local environments, since the local decoherence of any particle would cause the collapse of the whole cat state. Therefore, it is unclear whether the sub-Heisenberg scaling of quantum critical metrology is robust against the local decoherence. Here we study the effects of local decoherence on the quantum critical metrology, using a one-dimensional transverse-field Ising model as a representative example. Based on a previous work [Phys. Rev. Lett. 94, 047201 (2005)] on the critical behaviors of the noisy Ising model, which shows that the universality class of the quantum criticality is modified by the decoherence, we find that the standard quantum limit is recovered by the single-particle decoherence, which is equivalent to local quantum measurement conducted by the environment and destroys the many-body entanglement in the ground state at the quantum critical point. Following the renormalization group analysis [Phys. Rev. B 69, 054426 (2004)], we argue that the noise effects on quantum critical metrology should be universal. This works demonstrates the importance of protecting macroscopic quantum coherence for quantum sensing based on critical behaviors.
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