Understanding And Improving Critical Metrology. Quenching Superradiant Light-Matter Systems Beyond The Critical Point

Abstract

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.

Featured image: The schematic represents a toy model for a quantum phase transition ($g/g_c>1$ is the superradiant phase), with the black line being the effective potential that is felt by a quantum state (dashed-gray line). Driving the system close to the critical point ($g/g_c sim 1)$ creates the correlated (squeezed) excitations at a very slow rate (critical slowing down), since the effective potential is still of trapping form. However, if the system is quenched beyond the critical point ($g/g_c > 1$), the same number of correlated excitations can be generated much faster since the initial state will behave as if it was placed in an inverted harmonic oscillator potential. The purple ellipses represent the phase space picture of the state.

Popular summary

Quantum metrology makes use of non-classical correlations in order to make ultra precise measurements beyond the standard quantum limit. For example, operating state-of-the-art optical lattices at the ultimate Heisenberg limit of precision, one could keep time with an error of hundreds of milliseconds over the entire age of the universe.

Systems exhibiting quantum phase transitions have been the recent subject of intense focus due to their extreme sensitivity in the vicinity of the critical point. However, preparation of the critical ground state must be performed over long time scales in order to avoid excitations, which has so far resulted in sub-optimal scaling of sensitivity with time accounted for as a resource.

In our work, we depart from the traditional notion of metrology near a critical point, instead showing that sensitivity can be enhanced exponentially in a dynamical protocol by quenching past the critical point. We mathematically prove in the paradigmatic setting of cavity QED that a sensitivity exponentially growing in time can be obtained by quenching through a superradiant phase transition. We show that this is associated with a macroscopic occupation of the photonic mode, and that a basic homodyne detection scheme then yields the optimal measurement. Our result offers an exponential speed-up in time over existing protocols acting near the critical point in a general class of superradiant systems, and opens a new avenue for dynamical quantum metrology in critical systems.

► BibTeX data

@article{Gietka2022understanding, doi = {10.22331/q-2022-04-27-700}, url = {https://doi.org/10.22331/q-2022-04-27-700}, title = {Understanding and {I}mproving {C}ritical {M}etrology. {Q}uenching {S}uperradiant {L}ight-{M}atter {S}ystems {B}eyond the {C}ritical {P}oint}, author = {Gietka, Karol and Ruks, Lewis and Busch, Thomas}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {6}, pages = {700}, month = apr, year = {2022} }

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Cited by

[1] Louis Garbe, Obinna Abah, Simone Felicetti, and Ricardo Puebla, “Exponential precision by reaching a quantum critical point”, arXiv:2112.11264.

[2] Louis Garbe, Obinna Abah, Simone Felicetti, and Ricardo Puebla, “Critical quantum metrology with fully-connected models: from Heisenberg to Kibble-Zurek scaling”, Quantum Science and Technology 7 3, 035010 (2022).

[3] Karol Gietka, “Squeezing by critical speeding up: Applications in quantum metrology”, Physical Review A 105 4, 042620 (2022).

[4] Fabrizio Minganti, Louis Garbe, Alexandre Le Boité, and Simone Felicetti, “Non-Gaussian superradiant transition via three-body ultrastrong coupling”, arXiv:2204.03520.

[5] Enrico Rinaldi, Roberto Di Candia, Simone Felicetti, and Fabrizio Minganti, “Dispersive qubit readout with machine learning”, arXiv:2112.05332.

The above citations are from SAO/NASA ADS (last updated successfully 2022-06-03 03:38:05). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2022-06-03 03:38:04).

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.

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Understanding and Improving Critical Metrology. Quenching Superradiant Light-Matter Systems Beyond the Critical Point

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