Optical atomic magnetometry is a powerful tool for continuous sensing applications, yet, in the absence of quantum correlations, its sensitivity is limited by the standard quantum limit (SQL) stemming from a trade-off between optical probe imprecision and quantum measurement backaction. Beyond-SQL sensitivity requires quantum correlations that modify these measurement noise sources. Here we demonstrate such sensitivity by using entangled state of the probe light and by engineering correlations between measurement imprecision and backaction. Having first explored SQL in a broad range of frequencies, we demonstrate overcoming the limit by combining variational readout with coupling the magnetometer to one mode of a bipartite entangled light state and conditioning the results on the other entangled mode. Tuning the detected light quadratures and combining the signals from the two measurement channels, we achieve sensitivity beyond the SQL in a broad range of acoustic frequencies which has so far remained inaccessible to quantum-noise-limited optical magnetometry.
Optical atomic magnetometry is a powerful tool for continuous sensing applications, yet, in the absence of quantum correlations, its sensitivity is limited by the standard quantum limit (SQL) stemming from a trade-off between optical probe imprecision and quantum measurement backaction. Beyond-SQL sensitivity requires quantum correlations that modify these measurement noise sources. Here we demonstrate such sensitivity by using entangled state of the probe light and by engineering correlations between measurement imprecision and backaction. Having first explored SQL in a broad range of frequencies, we demonstrate overcoming the limit by combining variational readout with coupling the magnetometer to one mode of a bipartite entangled light state and conditioning the results on the other entangled mode. Tuning the detected light quadratures and combining the signals from the two measurement channels, we achieve sensitivity beyond the SQL in a broad range of acoustic frequencies which has so far remained inaccessible to quantum-noise-limited optical magnetometry.
Interferometers enable ultrasensitive measurement in a wide array of applications from gravitational wave searches to force microscopes. The role of quantum mechanics in the metrological limits of interferometers has a rich history, and a large number of techniques to surpass conventional limits have been proposed. In a typical measurement configuration, the trade-off between the probe’s shot noise (imprecision) and its quantum backaction results in what is known as the standard quantum limit (SQL). In this work, we investigate how quantum correlations accessed by modifying the readout of the interferometer can access physics beyond the SQL and improve displacement sensitivity. Specifically, we use an optical cavity to probe the motion of a silicon nitride membrane off mechanical resonance, as one would do in a broadband displacement or force measurement, and observe sensitivity better than the SQL dictates for our quantum efficiency. Our measurement illustrates the core idea behind a technique known as variational readout, in which the optical readout quadrature is changed as a function of frequency to improve broadband displacement detection. And, more generally, our result is a salient example of how correlations can aid sensing in the presence of backaction.
Abstract In the last few decades, the atomic magnetometry [1–7] has experienced remarkable development and reached to an outstanding sensitivity. This exciting technology is finding applications in various of fields [8–18]. The last two obstacles to further improve the sensitivity of magnetometry are quantum fluctuations and ambient magnetic field. For magnetometry based on optical readout of atomic ensemble’s spin precession, the fundamental limitation of sensitivity is restricted by spin projection noise (SPN) and photon shot noise (PSN). Meanwhile, in practical applications, ambient magnetic field noise which is regarded as a common-mode magnetic-field (CMM) noise is also limiting the sensitivity. Several techniques for reducing PSN [19–25], SPN [26, 27], and CMM noise [7, 28–31] have been proposed, respectively. To achieve the best sensitivity, it is essential to find an efficacious way to eliminate the noises from different sources, simultaneously. For this purpose, here we demonstrate a sub-shot-noise magnetic gradiometer utilizing entangled optical detection with quantum-correlated twin beams. This leads to the simultaneous suppression of PSN and CMM noise. The quantum enhancement spans a frequency range from 7 Hz to 6 MHz with maximum squeezing of 5.5 dB below the standard quantum limit (SQL). The sensitivity of gradient magnetic field reaches 18 fT/cm√Hz at 20 Hz with these sophisticated techniques. Our study opens up new possibilities to use quantum-enhanced technology in developing sensitive magnetometry for practical applications with noisy and physically demanding environments.
When one seeks knowledge of the full dynamics of the displacement of a harmonic oscillator, non-commutation of the two mechanical quadratures requires a minimum added noise equal to the mechanical resonator's zero point motion. This fundamental quantum limit (QL) is a distinct bound from the standard quantum limit (SQL) that is often considered in interferometric displacement measurement. The SQL is a consequence of the non-commutation of the probe's quadratures in a specific measurement configuration and is characterized by a tradeoff between shot noise (SN) imprecision and quantum backaction that are uncorrelated. The QL and SQL reach the same limit when probing at the peak mechanical response, but the QL can be a significantly lower bound off resonance. In studies of micro-mechanical motion, there has been great interest in observing quantum backaction and approaching the SQL on mechanical resonance. However, much of what historically motivates SQL research is displacement monitoring over a wide frequency band, such as gravitational wave searches. One long-standing concept for surpassing the SQL is to introduce correlations by changing the readout quadrature as a function of frequency in a technique known as variational readout. Here we harness quantum correlations in the measurement of a macroscopic resonator by modifying the readout quadrature of an optical interferometer. By using an optomechanical device thermalized to a dilution refrigerator, we measure quantum noise far off resonance where we improve upon the off-resonance SQL for our quantum efficiency.
We study quantum enhancement of sensitivity using squeezed light in a multiparameter quantum sensor, the hybrid dc and rf optically pumped magnetometer (hOPM) [M. Lipka , Multiparameter quantum sensing and magnetic communication with a hybrid dc and rf optically pumped magnetometer, , 034054 (2024)]. Using a single spin ensemble, the hOPM acquires both the dc field strength (scalar magnetometry) and resonantly detects one quadrature of the ac magnetic field at a chosen frequency (rf magnetometry). In contrast to the Bell-Bloom scalar magnetometer [C. Troullinou , Squeezed-light enhancement and backaction evasion in a high sensitivity optically pumped magnetometer, , 193601 (2021)], the backaction evasion in the hOPM is incomplete, leading to a nontrivial interplay of the three quantum noise sources in this system: photon shot noise, spin projection noise, and measurement backaction noise. We observe these interactions using squeezed light as a tool to control the distribution of optical quantum noise between S 2 and S 3 polarization Stokes components, and the resulting effect on readout quantum noise and measurement backaction. These results demonstrate quantum-enhanced sensitivity in a continuously operating multiparameter sensor and reveal fundamental trade-offs between sensitivity, backaction, and bandwidth.
Measurements with quantum limited resolution have important applications in metrology and sensing, including atomic clocks, atom interferometry, and magnetometry. We perform a quantum-non-demolition measurement on a collective angular momentum of a million spin-4 Cs atoms with high optical depth in our work. Quantum mechanics limits the measurement's resolution to what is known as the standard quantum limit (SQL) when there is no entanglement between the individual atoms. We can generate entanglement between atoms to create spin squeezed states through quantum backaction, improving the measurement sensitivity by 5.5 dB relative to the SQL. We have recently rebuilt the entire experiment inside a state-of-the-art magnetic shield of mu-metal and aluminum. This upgrade has drastically mitigated classical control errors in the spin squeezing experiment. Furthermore, the ensemble's sensitivity to magnetic fields allows us to make precise measurements of the magnetic field environment. Using closed-loop feedback, we use our atomic magnetometer to measure magnetic fields 4.3 dB below the SQL. The shielded environment will allow us to optimize the magnetometer and sets the stage for future experiments to use the closed-loop control to explore more complicated quantum dynamics.
Quantum mechanics places noise limits and sensitivity restrictions on physical measurements. The balance between unwanted backaction and the precision of optical measurements impose a standard quantum limit (SQL) on interferometric systems. In order to realize a sensitivity below the SQL, it is necessary to leverage a back-action evading measurement technique, or else exploit cancellations of any excess noise contributions at the detector. %Many proof of principle experiments have been performed, but only recently has an experiment achieved sensitivity below the SQL. In this work, we extend that initial demonstration and realize sub-SQL measurement sensitivity nearly two times better than previous measurements, and with architecture applicable to interferometric gravitational wave detectors. In fact, this technique is directly applicable to Advanced LIGO, which could observe similar effects with a detuned signal recycling cavity. By exploiting quantum correlations created by an optical spring, we measure a total sensitivity below the SQL by 2.8 dB, corresponding to a reduction in the noise power by 72±5.1 \% below the quantum limit. Through the use of a detuned optical spring, this noise reduction is tunable, allowing us to choose the desired range of frequencies that fall below the SQL. This result demonstrates access to sensitivities well below the SQL at frequencies ranges applicable to LIGO, with the potential to extend the reach of gravitational wave detectors further into the universe.