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Exponentially Enhanced Quantum Metrology by Quenching Superradiant Light-Matter Systems Beyond the Critical Point.

Karol Gietka, Lewis Ruks, Thomas Busch

Published Nov 16, 2021• 0 citations
OpenAlex

Abstract

We present a quantum metrology protocol which relies on quenching a light-matter system exhibiting a superradiant quantum phase transition beyond its critical point. In the thermodynamic limit these systems can exhibit an exponential divergence of the quantum Fisher information in time, whose origin is the exponential growth of the number of correlated photons on an arbitrarily fast time scale determined by the coupling strength. This provides an exponential speed-up in the growth of the quantum Fisher information over existing critical quantum metrology protocols relying on quenching close to the critical point and observing power law behaviour. We demonstrate that the Cram\'er-Rao bound can be saturated in our protocol through the standard homodyne detection scheme. We explicitly show its advantage using the archetypal setting of the Dicke model and explore a quantum gas coupled to a single-mode cavity field as a potential platform. In this case an additional exponential enhancement of the quantum Fisher information can in practice be observed with the number of atoms $N$ in the cavity, even in the absence of $N$-body coupling terms.

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We present a quantum metrology protocol which relies on quenching a light-matter system exhibiting a superradiant quantum phase transition beyond its critical point. In the thermodynamic limit these systems can exhibit an exponential divergence of the quantum Fisher information in time, whose origin is the exponential growth of the number of correlated photons on an arbitrarily fast time scale determined by the coupling strength. This provides an exponential speed-up in the growth of the quantum Fisher information over existing critical quantum metrology protocols relying on quenching close to the critical point and observing power law behaviour. We demonstrate that the Cram'er-Rao bound can be saturated in our protocol through the standard homodyne detection scheme. We explicitly show its advantage using the archetypal setting of the Dicke model and explore a quantum gas coupled to a single-mode cavity field as a potential platform. In this case an additional exponential enhancement of the quantum Fisher information can in practice be observed with the number of atoms NNN in the cavity, even in the absence of NNN-body coupling terms.
We present a quantum metrology protocol which relies on quenching a light-matter system exhibiting a superradiant quantum phase transition beyond its critical point. In the thermodynamic limit these systems can exhibit an exponential divergence of the quantum Fisher information in time, whose origin is the exponential growth of the number of correlated photons on an arbitrarily fast time scale determined by the coupling strength. This provides an exponential speed-up in the growth of the quantum Fisher information over existing critical quantum metrology protocols observing power law behaviour. We demonstrate that the Cramer-Rao bound can be saturated in our protocol through the standard homodyne detection scheme. We explicitly show its advantage in the archetypal setting of the Dicke model and explore a quantum gas coupled to a single-mode cavity field as a potential platform. In this case an additional exponential enhancement of the quantum Fisher information can in practice be observed with the number of atoms NNN in the cavity, despite existing works suggesting a requirement of NNN-body coupling terms.
We carefully examine critical metrology and present an improved critical quantum metrology protocol which relies on quenching a system exhibiting a superradiant quantum phase transition beyond its critical point. We show that this approach can lead to an exponential increase of the quantum Fisher information in time with respect to existing critical quantum metrology protocols relying on quenching close to the critical point and observing power law behaviour. We demonstrate that the Cramér-Rao bound can be saturated in our protocol through the standard homodyne detection scheme. We explicitly show its advantage using the archetypal setting of the Dicke model and explore a quantum gas coupled to a single-mode cavity field as a potential platform. In this case an additional exponential enhancement of the quantum Fisher information can in practice be observed with the number of atoms N in the cavity, even in the absence of N -body coupling terms.
Quantum metrology shows that by exploiting nonclassical resources it is possible to overcome the fundamental limit of precision found for classical parameter-estimation protocols. The scaling of the quantum Fisher information -- which provides an upper bound to the achievable precision -- with respect to the protocol duration is then of primarily importance to assess its performances. In classical protocols the quantum Fisher information scales linearly with time, while typical quantum-enhanced strategies achieve a quadratic (Heisenberg) or even higher-order polynomial scalings. Here we report a protocol that is capable of surpassing the polynomial scaling, and yields an exponential advantage. Such exponential advantage is achieved by approaching, but without crossing, the critical point of a quantum phase transition of a fully-connected model in the thermodynamic limit. The exponential advantage stems from the breakdown of the adiabatic condition close to a critical point. As we demonstrate, this exponential scaling is well captured by the new bound derived in arXiv:2110.04144, which in turn allows us to obtain approximate analytical expressions for the quantum Fisher information that agree with exact numerical simulations. In addition, we discuss the limitations to the exponential scaling when considering a finite-size system as well as its robustness against decoherence effects. Hence, our findings unveil a novel quantum metrological protocol whose precision scaling goes beyond the paradigmatic Heisenberg limit with respect to the protocol duration.
Critical metrology relies on the precise preparation of a system in its ground state near a quantum phase transition point where quantum correlations get very strong. Typically, this increases the quantum Fisher information with respect to changes in system parameters and thus improves the optimally possible measurement precision limited by the Cramér-Rao bound. Hence critical metrology involves encoding information about the unknown parameter in changes of the system's ground state. Conversely, in conventional metrology methods like Ramsey interferometry, the eigenstates of the system remain unchanged, and information about the unknown parameter is encoded in the relative phases that excited system states accumulate during their time evolution. Here we introduce an approach combining these two methodologies into a unified protocol applicable to closed and driven-dissipative systems. We show that the quantum Fisher information in this case exhibits an additional interference term originating from the interplay between eigenstate and relative phase changes. We provide analytical expressions for the quantum and classical Fisher information in such a setup, elucidating as well a straightforward measurement approach that nearly attains the maximum precision permissible under the Cramér-Rao bound. We showcase these results by focusing on the squeezing Hamiltonian, which characterizes the thermodynamic limit of Dicke and Lipkin-Meshkov-Glick Hamiltonians.
Quantum metrology refers to the use of quantum resources in parameter-estimation protocols, aiming at enhancing its precision. The quantum Fisher information is a key quantity in this context, setting the ultimate achievable precision with respect to available resources, such as the total time of the protocol. In this work, we report a scheme where the quantum Fisher information features an exponential scaling with the protocol duration. This is achieved by performing a periodic modulation of the coupling of a quantum critical system close to the its critical value. This modulation leads to an exponential growth of the excitation number in time. Relying on the precision bound derived by Garbe et al. [L. Garbe et al., Quantum Sci. Technol. 7, 035010 (2022)], we show that the quantum Fisher information inherits this exponential time scaling, which is corroborated by numerical simulations. Finally, the impact of dissipation and finite-size effects are analyzed, showing that the exponential time scaling is robust to dissipation, although its exponent decreases for larger values of the dissipation rate. Therefore, our work illustrates the novel metrological opportunities that quantum critical systems can offer.
Critical quantum metrology aims to harness critical properties near quantum phase transitions to enhance parameter estimation precision. However, critical slowing down inherently limits the achievable precision within a finite evolution time. To address this challenge, we establish a fundamental scaling limit of critical quantum metrology with respect to the total evolution time. We find that the effective winding number of the system's phase-space trajectory determines the scaling bound of quantum Fisher information. Furthermore, we demonstrate that the exponential scaling of the quantum Fisher information can be obtained, and for this, it is necessary to increase the effective winding number by the total evolution time. Based on the topological nature of the effective winding number, we explicitly derive an optimal time-dependent control whose form is, surprisingly, a simple on-off scheme. We highlight that such an exponential scaling of quantum Fisher information remains valid even without reaching the critical point and in the presence of thermal dissipation, albeit with a decreased exponent.