Sub-shot-noise Rydberg EIT spectrum

Coherent population oscillations spectroscopy, which is based on the interaction between atoms and the phase locked laser, is a kind of atomic population modulation spectroscopy. When the laser frequency difference is less than natural width of energy level, the coherent oscillation of atomic population will be induced by laser intensity modulation so that the probe laser transmission with narrow bandwidth can be realized. For a closed two-level system (TLS), the spectral line-width is limited mainly by the spontaneous emission lifetime of the upper atomic energy level. As for a three-level atomic system of Λ configuration, the two linearly polarized beams with both σ+ and σ- polarization component, the laser-atom interaction satisfies the selection rule. The spectral line-width mainly depends on the ground-state relaxation time, and the dependence on the line-width of spontaneous radiation is eliminated. In this paper, the laser from a external-cavity diode laser has its frequency locked to Cesium <inline-formula><tex-math id="M1">\begin{document}$6{{\rm{S}}_{1/2}}\left( {F = 3} \right) \to 6{{\rm{P}}_{3/2}}\left( {F' = 3} \right)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20210405_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20210405_M1.png"/></alternatives></inline-formula> transition. The frequencies of the two beams are shifted down by two independent double-passed acousto-optic modulators (AOM) to nearly resonate to Cesium <inline-formula><tex-math id="M2">\begin{document}$6{{\rm{S}}_{1/2}}\left( {F = 3} \right) \to 6{{\rm{P}}_{3/2}}\left( {F' = 2} \right)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20210405_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20210405_M2.png"/></alternatives></inline-formula> transition. The probe beam and the coupling beam are superposed at polarization beam splitter (PBS) cube and transmitted through the magnetically shielded cesium vapor cell in the same direction. The two beams have approximately the same Gaussian diameter of 6.6 mm. The beams are separated by another PBS behind the vapor cell, and the probe beam is detected by a photodiode. We realize the coherent population oscillation spectroscopy through the Cesium vapor cell at room temperature without buffer gas. The spectral linewidth is typically less than 50 kHz which is far below the spontaneous radiation linewidth(~5.2 MHz). The linewidth of coherent population oscillation spectroscopy of the Λ-type atomic energy level structure depends only on the population associated with the oscillation of multiple degenerate level systems except phase correlations of atomic states. Coherent population oscillation is beneficial to the obtaining of the narrow linewidth spectroscopy through the Rydberg atomic system with long excited state lifetime. Considering the importance of electric field measurement using Rydberg atoms, the method of coherent population oscillation can be used to improve the sensitivity of precise measurements based on Rydberg atoms.

Rydberg atoms have demonstrated exceptional capabilities in the precise sensing microwave (MW) fields. Previous studies on Rydberg atom-based electrometers (RAEs) have predominantly focused on absorption measurements. Recently, phase-sensitive RAEs employing Mach-Zehnder interferometer (MZI) have been demonstrated, though their performance remains constrained by the standard quantum limit (SQL). In this study, we combine RAEs with advanced quantum interferometrics to enhance MW field sensing. Within the framework of electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting, the noise of our enhanced electrometer is suppressed below the photon shot noise (PSN) in measuring light dispersion through microwave-dressed atoms, when utilizing phase squeezed states. In our theory, the optimal sensitivity of the MW field can reach 1.36 × 10-11V/m/Hz1/2 with a dressed MW field strength of 2.4 × 10-4V/m within a balanced SU(1,1) interferometer.

It is shown that photon shot noise and radiation-pressure back-action noise are the sole forms of quantum noise in interferometric gravitational wave detectors that operate near or below the standard quantum limit, if one filters the interferometer output appropriately. No additional noise arises from the test masses' initial quantum state or from reduction of the test-mass state due to measurement of the interferometer output or from the uncertainty principle associated with the test-mass state. Two features of interferometers are central to these conclusions: (i) The interferometer output (the photon number flux N(t) entering the final photodetector) commutes with itself at different times in the Heisenberg Picture, [N(t), N(t')] = 0, and thus can be regarded as classical. (ii) This number flux is linear in the test-mass initial position and momentum operators x_o and p_o, and those operators influence the measured photon flux N(t) in manners that can easily be removed by filtering -- e.g., in most interferometers, by discarding data near the test masses' 1 Hz swinging freqency. The test-mass operators x_o and p_o contained in the unfiltered output N(t) make a nonzero contribution to the commutator [N(t), N(t')]. That contribution is cancelled by a nonzero commutation of the photon shot noise and radiation-pressure noise, which also are contained in N(t). This cancellation of commutators is responsible for the fact that it is possible to derive an interferometer's standard quantum limit from test-mass considerations, and independently from photon-noise considerations. These conclusions are true for a far wider class of measurements than just gravitational-wave interferometers. To elucidate them, this paper presents a series of idealized thought experiments that are free from the complexities of real measuring systems.

Rydberg atoms are highly excited atoms with large principal quantum number n, big sizes (~n2) and long lifetimes (~n3). Rydberg atoms are very sensitive to an external field due to the large polarizabilities of Rydberg atoms (~n7). Electromagnetically induced transparency (EIT) of Rydberg atom provides an ideal method to detect Rydberg atoms without destroying atoms, and can be used to measure the external direct current and radio frequency (RF) field. In this paper, we study the EIT effect of a cesium ladder-type three-level atom involving Rydberg state exposed to a weak RF field. The ground state (6S1/2), the excited state (6P3/2) and Rydberg state (48D5/2) constitute the Rydberg three-level system, in which the probe laser couples 6S1/2(F=4)6P3/2(F'=5) transition, whereas the coupling laser scans across the 6P3/248D5/2 Rydberg transition. The coupling laser (510 nm laser, propagating in the z-axis direction and linear polarization in the y-axis direction) and the probe laser (852 nm laser, linear polarization in the y-axis direction) counter-propagate through a 50-mm-long cesium vapor cell at room temperature, yielding Rydberg EIT spectra. Rydberg EIT signal is detected as a function of the detuning of the coupling laser. When a weak RF (80 MHz) electric field polarized in the x-axis direction is applied to a pair of electrode plates located on both sides of the cesium cell, the EIT spectrum of Rydberg 48D5/2 shows the Stark splitting and the even order harmonic sidebands. The experimental results are analyzed by using the Floquet theory. The simulation results accord well with the experimentally measured results. Furthermore, we also investigate the influence of the self-ionization effect of Rydberg atom on the Stark spectrum by changing the RF frequency. We put forward a proposal to avoid the effect of ionization by placing electrode plates in the cesium cell. In the weak RF-field domain, mj=5/2 Stark line crosses mj=1/2, 3/2 sidebands, these cross points provide an antenna-free method of accurately calibrating the RF electric field based on Rydberg atoms.

The interaction of many-body quantum system is a critical problem to be solved in the field of quantum information science. Rydberg atoms have large dipole moment, enabling them to interact with others in a long range, thereby offering us a powerful tool for studying many-body quantum physics. Meanwhile, atoms in the ground state are stable, which makes it easy to manipulate them. Therefore, Rydberg-atom many-body system is an ideal platform for studying the interaction of many-body quantum system. Studies of Rydberg-atom many-body system may contribute to understanding the properties of many-body system and putting the interaction of many-body quantum system into practical applications. In this review, we introduce some studies of properties of interaction of Rydberg-atom many-body system, including the Rydberg excitation blockade, the variation of Rabi frequencies of the many-body system and special spatial distribution of Rydberg atoms in a many-body system. Firstly, the Rydberg excitation blockade, the most important property in the Rydberg-atom many-body system, indicates that atoms’ excitation will be suppressed in a certain range around one Rydberg excitation because the interaction between the Rydberg excitation and atoms leads the energy level to shift so that atoms cannot be excited by the same pulse. Secondly, there is a collective Rabi frequency in the system, which is proportional to the square of the number of atoms in the suppressed area. And additionally, because of the Rydberg blockade effect, Rydberg excitations in the ensemble cannot be at casual positions but a regular distribution is formed. Besides the studies of properties, several researches on the applications of interaction of Rydberg-atom many-body system are introduced, including single-photon source, quantum storage, single-atom imaging, quantum simulation, etc. These applications contribute to the development of quantum community and quantum computing, which may bring us a quantum-technology time. Finally, we discuss the future development of Rydberg-atom many-body system and its further applications. Further development includes the development of many-body system with a larger number of atoms, the development of many-body system of atoms with more than one electron, and some other specific subjects based on many-system, such as Rydberg dimer and topological phase. Also some promising applications such as in studying optimization problem by quantum annealing, may become true.

The uncertainty principle, applied naively to the test masses of a laser-interferometer gravitational-wave detector, produces a standard quantum limit (SQL) on the interferometer's sensitivity.It has long been thought that beating this SQL would requirea radical redesign of interferometers. However, we show that LIGO-II interferometers, currently planned for 2006, can beat the SQL by as much as a factor two over a bandwidth Δf~f,if their thermal noise can be pushed low enough. This is due todynamical correlations between photon shot noise and radiation-pressure noise, produced by the LIGO-II signal-recycling mirror.

Optical rotation detection system (ORDS) utilizing quantum nondemolition (QND) measurement methods is widely applied in the field of quantum metrology and quantum information. However, the sensitivity of ORDS is limited by the uncertainty from optical-couple noise during the measurement of the atomic spin ensemble. In this study, we specifically analyze the mechanism of optical-couple noise caused by the fluctuations of probe light's polarization in the modulated ORDS with a new model established to describe atomic spin precession in this particular condition. It is discovered that transverse electron-spin polarization errors are generated by the residual probe photon spin polarization in the ORDS, which results in extra coupling magnetic noise. In order to suppress this noise, a novel in situ method is proposed that the resultant electron-spin errors are reduced by a specifically designed closed-loop system. The results are verified through the ORDS in a co-magnetometer. After zeroing the extra probe photon spin polarization, an angular sensitivity better than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1 \times 10 ^{\mathrm {-8}}$ </tex-math></inline-formula> rad/Hz <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\mathrm {1/2}}$ </tex-math></inline-formula> is achieved for frequencies higher than 5 Hz, demonstrating a probe background noise of 0.26 fT/Hz <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\mathrm {1/2}}$ </tex-math></inline-formula> @14.5 Hz, approaching electronic noise and photon shot noise (PSN). With closed-loop control, the optical rotation bias instability is promoted by 4.2 times (from 107.9 to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$25.7 \mu $ </tex-math></inline-formula> rad/h), and the angular noise of the ORDS is reduced by 2.4 times at 1–100 Hz. The measurement uncertainty of the realized ORDS nears the standard quantum limit, paving the road for long-term ultrasensitive measurements for new physics explorations.

A Rydberg atom is an atom excited to a high energy level, and there is a strong dipole-dipole interaction between nearby Rydberg atoms. While there has been much interest in closed systems of Rydberg atoms, less is known about open systems of Rydberg atoms with spontaneous emission. This thesis explores the latter. We consider a lattice of atoms, laser-excited from the ground state to a Rydberg state and spontaneously decaying back to the ground state. Using mean-field theory, we study the how the steady-state Rydberg population varies across the lattice. There are three phases: uniform, antiferromagnetic, and oscillatory. Then we consider the dynamics of the quantum model when mean-field theory predicts bistability. Over time, the system occasionally jumps between a state of low Rydberg population and a state of high Rydberg population. We explain how entanglement and quantum measurement enable the jumps, which are otherwise classically forbidden. Finally, we let each atom be laser-excited to a short-lived excited state in addition to a Rydberg state. This three-level configuration leads to rich spatiotemporal dynamics that are visible in the fluorescence from the short-lived excited state. The atoms develop strong spatial correlations that change on a long time scale.

Cavity optomechanics with feedback and fluids

A microwave single-photon detector was developed with highly-excited alkaline Rydberg-atoms in a cooled resonant cavity to search for dark matter axions. This detector belongs to a microwave single-photon counter, thus being free from the standard quantum limit (SQL). High sensitivity of the present detector system was demonstrated by measuring the thermal blackbody radiations in the cavity at temperatures as low as 70 mK where the sensitivity is below the SQL. The detection sensitivity of the present system is mainly limited by stray electric fields present in the detection region. Practical design of a new experimental scheme with a guiding electric field through the atomic-beam trajectory is here presented and discussed to avoid the effect of stray electric field and thus to improve the detection sensitivity.

A high-sensitivity microwave-single-photon detector was developed in Kyoto, in which microwave photons in a resonant cavity cooled at very low temperatures are absorbed by highly excited Rydberg atoms and the Rydberg atoms thereby promoted to a higher excited state are then selectively field-ionized and detected. This scheme allows us to count microwave photons one by one, thus provide a single-photon counting without the limit of standard quantum limit (SQL). The apparatus “CARRACK” for the single-photon detector was constructed based on this scheme, where the cavity was cooled down to 10 mK range to reduce the background of thermal blackbody photons from the cavity wall. The apparatus has served for years to search for dark matter axions in the 10 μeV (∼2.4 GHz) mass region. Thermal blackbody photons in a microwave resonant cavity at temperatures as low as 70 mK have been measured, the sensitivity being below the SQL limit. A number of improvements in the detection efficiency and sensitivity have been planned and will be reported. Applications of the detector to fundamental physics are also discussed shortly.

Rydberg atoms have stood out as a highly promising platform for realizing quantum computation. Floquet frequency modulation (FFM), in Rydberg atom systems, provides a unique tool for achieving precise quantum control and uncovering exotic physical phenomena. This work introduces a method to realize controlled arbitrary phase gates in Rydberg atoms by manipulating system dynamics using FFM. Notably, the need for laser addressing of individual atoms is eliminated, enhancing convenience for practical applications. Furthermore, this approach is integrated with soft quantum control strategies to enhance the fidelity and robustness of the resultant controlled-phase gates. Finally, as an example, this methodology is applied in Grover-Long algorithm to search target items with zero failure rate, demonstrating its substantial significance for future quantum information processing applications. This work leveraging Rydberg atoms and FFM may herald a new era of scalable and reliable quantum computing.

In the past decade, impressive efforts have been powered in the field of optomechanics that is the study of the coupling between a light field and a mechanical degree of freedom, with the major aims of detecting the quantum zero-point motion fluctuations of a mechanical object, and studying the fundamental quantum measurement processes. Though having their own specificities, both aims require combining ultra-high sensitivity readout together with ultra-sensitive mechanical response, sharing for example the common condition to involve measurement schemes limited at a level better than that of the Standard Quantum Limit (SQL) [1]. Using optical readout, we demonstrate for the first time sub-SQL imprecision for nanomechanical motion at room temperature. By using a cavity optomechanical near-field coupling scheme with more than one order of magnitude improved optomechanical coupling coefficients [2] combined with homodyne detection we reach a room-temperature imprecision 3 dB below the SQL launching only 1 µW of optical input power (see Fig. 1).

We report a measurement beyond the standard quantum limit for displacement amplitude acting on a cavity field. As resource we use field entanglement with a Rydberg atom. Measurement optimality is proven by Fisher information analysis.

Fundamental quantum fluctuations caused by the Heisenberg principle limit measurement precision. If the uncertainty is distributed equally between conjugate variables of the meter system, the measurement precision cannot exceed the standard quantum limit. When the meter is a large angular momentum, going beyond the standard quantum limit requires non-classical states such as squeezed states or Schrödinger-cat-like states. However, the metrological use of the latter has been so far restricted to meters with a relatively small total angular momentum because the experimental preparation of these non-classical states is very challenging. Here we report a measurement of an electric field based on an electrometer consisting of a large angular momentum (quantum number J ≈ 25) carried by a single atom in a high-energy Rydberg state. We show that the fundamental Heisenberg limit can be approached when the Rydberg atom undergoes a non-classical evolution through Schrödinger-cat states. Using this method, we reach a single-shot sensitivity of 1.2 millivolts per centimetre for a 100-nanosecond interaction time, corresponding to 30 microvolts per centimetre per square root hertz at our 3 kilohertz 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 distance of about 100 micrometres with a megahertz bandwidth is within reach.