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arXiv:1602.02488

A quantum-enabled Rydberg atom electrometer

Adrien Facon, Eva-Katharina Dietsche, Dorian Grosso, S. Haroche, J. M. Raimond, M. Brune, S. Gleyzes

Published Feb 8, 2016• 1 citation

Abstract

There is no fundamental limit to the precision of a classical measurement. The position of a meter's needle can be determined with an arbitrarily small uncertainty. In the quantum realm, however, fundamental quantum fluctuations due to the Heisenberg principle limit the measurement precision. The simplest measurement procedures, involving semi-classical states of the meter, lead to a fluctuation-limited imprecision at the standard quantum limit. By engineering the quantum state of the meter system, the measurement imprecision can be reduced down to the fundamental Heisenberg Limit (HL). Quantum-enabled metrology techniques are thus in high demand and the focus of an intense activity. We report here a quantum-enabled measurement of an electric field based on this approach. We cast Rydberg atoms in Schrödinger cat states, superpositions of atomic levels with radically different polarizabilites. We use a quantum interference process to perform a measurement close to the HL, reaching a single-shot sensitivity of 1.2 mV/cm for a 100 ns interaction time, corresponding to 30 $μ$V/cm/Hz^(1/2) at our 3 kHz repetition rate. This highly sensitive, non-invasive space- and time-resolved field measurement extends the realm of electrometric techniques and could have important practical applications. Detection of individual electrons in mesoscopic devices at a ~100 $μ$m distance, with a MegaHertz bandwith is within reach.

DOI: 10.48550/arxiv.1602.02488

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There is no fundamental limit to the precision of a classical measurement. The position of a meter's needle can be determined with an arbitrarily small uncertainty. In the quantum realm, however, fundamental quantum fluctuations due to the Heisenberg principle limit the measurement precision. The simplest measurement procedures, involving semi-classical states of the meter, lead to a fluctuation-limited imprecision at the standard quantum limit. By engineering the quantum state of the meter system, the measurement imprecision can be reduced down to the fundamental Heisenberg Limit (HL). Quantum-enabled metrology techniques are thus in high demand and the focus of an intense activity. We report here a quantum-enabled measurement of an electric field based on this approach. We cast Rydberg atoms in Schrödinger cat states, superpositions of atomic levels with radically different polarizabilites. We use a quantum interference process to perform a measurement close to the HL, reaching a single-shot sensitivity of 1.2 mV/cm for a 100 ns interaction time, corresponding to 30

μ

V/cm/Hz^(1/2) at our 3 kHz repetition rate. This highly sensitive, non-invasive space- and time-resolved field measurement extends the realm of electrometric techniques and could have important practical applications. Detection of individual electrons in mesoscopic devices at a ~100

μ

m distance, with a MegaHertz bandwith is within reach.

We realize a non-invasive electrometer based on state engineering in a Rydberg hydrogenic manifold. A quantum interference process involving states with very different dipoles measures directly the time correlation of a stochastic electric field, with a 200~ns time resolution and with a

83.2\pm1.4

~mV/m single-atom sensitivity, beyond the Standard Quantum Limit in this context. This quantum-enabled correlation electrometer opens the way to applications in mesoscopic physics, e.g. for the study of individual charge transits in nano-structures.

The development of a microwave electrometer with inherent uncertainty approaching its ultimate limit carries both fundamental and technological significance. However, because of the thermal motion of atoms, the state-of-art Rydberg electrometer falls considerably short of the standard quantum limit by about three orders of magnitude. Here, we use an optically thin medium with approximately 5.2 × 10 5 laser-cooled atoms to implement the microwave heterodyne detection. By mitigating various noises and strategically optimizing the electrometer parameters, our study reduces the equivalent noise temperature by a factor of 20 and achieves an electric field sensitivity of 10.0 nV cm −1 Hz −1/2 , lastly reaching a factor of 2.6 above the standard quantum limit. Our work also provides valuable insights into the inherent capabilities and limitations of Rydberg electrometers, offering superior sensitivity in detecting weak microwave signals for numerous applications.

Rydberg-atom electrometry is a core technique in the development of highly sensitive quantum electric-field sensors. Its sensitivity based on atom-photon interaction is typically limited by photon shot-noise (PSN) and spectral broadenings. Here, we experimentally demonstrate a near PSN-limited Rydberg electrometry from a 85Rb atomic vapor cell. By engineering atomic coherence through control of residual magnetic fields and laser frequency noise, we achieve the Rydberg electromagnetically induced transparency (EIT) with the narrow linewidth of 1.6 MHz, yielding an enhanced spectral slope for high-sensitivity Rydberg-EIT electrometry. Under optimized superheterodyne detection conditions, we obtain an electric-field sensitivity of 12.5(8) nV cm^-1 Hz^-1/2 at 37 GHz, in close agreement with the calculated PSN limit. These results provide direct experimental evidence of the high-sensitive quantum electrometry and establish a practical route toward quantum-noise-limited Rydberg electrometry.

A mesoscopic superposition of quantum states involving radiation fields with classically distinct phases was created and its progressive decoherence observed. The experiment involved Rydberg atoms interacting one at a time with a few photon coherent field trapped in a high

Q

microwave cavity. The mesoscopic superposition was the equivalent of an ``

\mathrm{atom}+\mathrm{measuring}\mathrm{apparatus}

'' system in which the ``meter'' was pointing simultaneously towards two different directions---a ``Schr\"odinger cat.'' The decoherence phenomenon transforming this superposition into a statistical mixture was observed while it unfolded, providing a direct insight into a process at the heart of quantum measurement.

Rydberg atoms have great potential in electric field measurement and have an advantage with a large frequency bandwidth from the kHz to the THz scale. However, the sensitivity for measuring a weak MHz electric field signal is limited by the spectroscopic resolution, because the weak electric field induces only a small perturbation of the population and energy-level shift of the Rydberg atoms. Here, we report highly sensitive measurement of a weak MHz electric field using electromagnetically induced transparency with Rydberg atoms in a thermal atomic system. Using the heterodyne method on a 30-MHz electric field, we successfully measure the minimum electric field strength to be $37.3\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{V}/\mathrm{cm}$ with a sensitivity up to $\ensuremath{-}65$ dBm/Hz and a linear dynamic range over 65 dB. Additionally, we measure an amplitude-modulated signal and demodulate the signal with a fidelity over 98%. This work extends the sensitivity of atomic sensors for measuring MHz electric fields, which advances atomic electric field-sensing technology.