Critical Quantum Metrology in the Non-Linear Quantum Rabi Model

Abstract

The quantum Rabi model (QRM) with linear coupling between light mode and qubit exhibits the analog of a second-order phase transition for vanishing mode frequency which allows for criticality-enhanced quantum metrology in a few-body system. We show that the QRM including a nonlinear coupling term exhibits much higher measurement precisions due to its first-order-like phase transition at finite frequency, avoiding the detrimental slowing-down effect close to the critical point of the linear QRM. When a bias term is added to the Hamiltonian, the system can be used as a fluxmeter or magnetometer if implemented in circuit QED platforms.

Scaling Relations and Topological Quadruple Points in Light‐Matter Interactions with Anisotropy and Nonlinear Stark Coupling

“…Note the few-body QPTs have a great potential for applications in critical quantum metrology. [36][37][38]68] Indeed, the regime around the QPT of the linear QRM provides a critical resource for high-precision measurements. While the linear QRM suffers from the limitation of one point of QPT, our phase diagrams demonstrate that the nonlinear QRM with the Stark coupling possesses a continuous and wide distribution range of QPTs which ensures a global high-precision resource for critical quantum metrology [92] while the scaling relations indicate that similar orders of high precision would be available under a scaling factor.…”

“…[36][37][38]68] Indeed, the regime around the QPT of the linear QRM provides a critical resource for high-precision measurements. While the linear QRM suffers from the limitation of one point of QPT, our phase diagrams demonstrate that the nonlinear QRM with the Stark coupling possesses a continuous and wide distribution range of QPTs which ensures a global high-precision resource for critical quantum metrology [92] while the scaling relations indicate that similar orders of high precision would be available under a scaling factor. On the other hand, it is recently found that the node number in the topological classification as discussed in the present work has a correspondence to spin windings and the spin texture changes sign at nodes, [95] which makes the topological information detectable.…”

“…A practical implication of our phase diagrams may lie in the few-body critical quantum metrology. [36][37][38]68] Few-body critical quantum sensors benefit from high controllability and do not suffer from the difficulty to reach equilibrium in thermodynamic systems. It has been shown that the QPT in the QRM can provide a high-precision resource for critical quantum metrology.…”

“…On the other hand, the milestone work of Braak revealing the integrability [ 3 ] of the quantum Rabi model (QRM), [ 17 ] which is a most fundamental model of light‐interactions, has triggered an intensive dialogue between mathematics and physics [ 18 ] and leads to a boom of theoretical developments. [ 4,5,19–63 ] Without mentioning the ubiquitous role of light‐matter interaction and its broad relevance to quantum optics, quantum information and quantum computation, [ 1,64–67 ] quantum metrology, [ 36–38,68 ] condensed matter, [ 2,27,28 ] and relativistic systems, [ 69 ] the explosively‐growing investigations have yielded abundant findings in the QRM and its extensions, such as hidden symmetry, [ 60–63 ] various patterns of symmetry breaking, [ 26,27,29 ] few‐body quantum phase transitions, [ 5,22–29,70 ] multicriticalities and multiple points, [ 26–28 ] universality classification, [ 24,25,27,52 ] spectral collapse, [ 33–35,45,48 ] photon blockade effect, [ 39,40 ] spectral conical intersections, [ 42 ] classical‐quantum correspondence, [ 41 ] single‐qubit conventional and unconventional topological phase transitions, […”

“…2g s as indicated by Equation ( 25), which can provide a global critical resource for the few-body quantum metrology. [92]…”