Quantum Projection Noise Limit Research Articles

Gravity measurement at the sub-millimeter scale with optical lattice clock

Due to the excellent accuracy, the optical lattice clock (OLC) has not only achieved impressive results in frequency measurement but also gradually plays an important role in quantum precision measurement. In this paper, we propose a scheme for measuring gravity at the sub-millimeter scale extracted from the Rabi spectrum based on Super-Bloch oscillations of atoms in the OLC. Our proposal can be realized on the existing OLC platform without significant change. Under realistic existing experimental parameters of 87Sr OLC, we determine the optimal experimental conditions and obtain a sensitivity of 5μGal/Hz in the quantum projection noise limit, which is 50 times better than the previous method at the sub-millimeter scale under the same consideration. Another advantage of our proposal is that it is insensitive to the noise of the lattice laser, which contributes to the major uncertainty of the previous measurement (PRA 86, 033615). Our research will promote the development of OLC geoscopy.

Distributed quantum sensing with mode-entangled spin-squeezed atomic states.

Quantum sensors are used for precision timekeeping, field sensing and quantum communication1-3. Comparisons among a distributed network of these sensors are capable of, for example, synchronizing clocks at different locations4-8. The performance of a sensor network is limited by technical challenges as well as the inherent noise associated with the quantum states used to realize the network9. For networks with only spatially localized entanglement at each node, the noise performance of the network improves at best with the square root of the number of nodes10. Here we demonstrate that spatially distributed entanglement between network nodes offers better scaling with network size. A shared quantum nondemolition measurement entangles a clock network with up to four nodes. This network provides up to 4.5 decibels better precision than one without spatially distributed entanglement, and 11.6 decibels improvement as compared to a network of sensors operating at the quantum projection noise limit. We demonstrate the generality of the approach with atomic clock and atomic interferometer protocols, in scientific and technologically relevant configurations optimized for intrinsically differential comparisons of sensor outputs.

Enhanced cold mercury atom production with two-dimensional magneto-optical trap

A cold atom source is important for quantum metrology and precision measurement. To reduce the quantum projection noise limit in optical lattice clock, one can increase the number of cold atoms and reduce the dead time by enhancing the loading rate. In this work, we realize an enhanced cold mercury atom source based on a two-dimensional (2D) magneto-optical trap (MOT). The vacuum system is composed of two titanium chambers connected with a differential pumping tube. Two stable cooling laser systems are adopted for the 2D-MOT and the three-dimensional (3D)-MOT, respectively. Using an optimized 2D-MOT and push beam, about 1.3×106 atoms, which are almost an order of magnitude higher than using a pure 3D-MOT, are loaded into the 3D-MOT for 202Hg atoms. This enhanced cold mercury atom source is helpful in increasing the frequency stability of a neutral mercury lattice clock.

Compact differential gravimeter at the quantum projection-noise limit

Atom interferometry offers new perspectives for geophysics and inertial sensing. We present the industrial prototype of a new type of quantum-based instrument: a compact, transportable, differential quantum gravimeter capable of measuring simultaneously the absolute values of both gravitational acceleration, $g$, and its vertical gradient, $\Gamma_{zz}$. While the sensitivity to g is competitive with the best industrial gravimeters, the sensitivity on $\Gamma_{zz}$ reaches the limit set by quantum projection noise-leading to an unprecedented long-term stability of 0.1 E ($1E=1\times 10^{-9}s^{-2}$). This unique, dual-purpose instrument, paves the way for new applications in geophysics, civil engineering, and gravity-aided navigation, where accurate mapping of the gravitational field plays an important role.

Longitudinal Ramsey spectroscopy of atoms for continuous operation of optical clocks

We propose a longitudinal Ramsey spectroscopy of atoms in a moving optical lattice. Spatially separated magnetic fields, which open the forbidden transition by mixing with the dipole-allowed states, create Ramsey pulses for a probe laser introduced along the optical lattice. Excitation of atoms in the Lamb-Dicke regime by a single probe laser avoids residual Doppler effects as well as mechanical instabilities that deteriorate Ramsey spectroscopy on an atomic beam. Continuous measurement and control of the probe laser improves the Allan deviation as τ −1 for an averaging time τ until the quantum projection noise limit is reached. For 88Sr atoms with an atomic flux of 104 s−1, we speculate a clock instability of 5 × 10−16(τ s−1)−1 down to its floor at around 10−18.

Quantum sensing of intermittent stochastic signals

Realistic quantum sensors face a trade-off between the number of sensors measured in parallel and the control and readout fidelity $(F)$ across the ensemble. We investigate how the number of sensors and fidelity affect sensitivity to continuous and intermittent signals. For continuous signals, we find that increasing the number of sensors by $1/{F}^{2}$ for $F<1$ always recovers the sensitivity achieved when $F=1$. However, when the signal is intermittent, more sensors are needed to recover the sensitivity achievable with one perfect quantum sensor. We also demonstrate the importance of near-unity control fidelity and readout at the quantum projection noise limit by estimating the frequency components of a stochastic, intermittent signal with a single trapped ion sensor. Quantum sensing has historically focused on large ensembles of sensors operated far from the standard quantum limit. The results presented in this paper show that this is insufficient for quantum sensing of intermittent signals and reemphasizes the importance of the unique scaling of quantum projection noise near an eigenstate.

Improvement in the stability of a 40Ca+ ion optical clock using the Ramsey method

The fractional uncertainty of the 40Ca+ optical clock in our laboratory has been evaluated to be 2.2×10−17, but it is difficult to evaluate the statistical uncertainty of the output frequency at this level, limited by the frequency stability associated with the quantum projection noise (QPN). A reduction in the stability is required to shorten the averaging time for a certain statistical uncertainty level. To improve the stability, the Ramsey method is introduced in the locking process. To improve the reliability and continuity, we introduce the idea of using auxiliary Rabi probes to avoid fringe slips in the Ramsey interrogation and to automatically search for resonance. The stability of a single 40Ca+ ion frequency standard is improved from 6.3×10−15/τ to 2.5×10−15/τ, where τ is the averaging time in seconds, which is close to the QPN limit for an 80-ms-long Ramsey interrogation. We obtain a stability of 1.5×10−17 at an averaging time of 21 000 s and an uptime rate of 93.8% for a 34-h-long run. These methods can easily be applied to other ion or neutral atom optical clocks.

Investigation and improvement of the spin self-sustaining magnetometer

The spin self-sustaining atomic magnetometer has the advantage of 1/τ measurement and great development potential in many applications. In this paper, we investigated the main elements that affect the stability and accuracy of the self-sustaining magnetometer and proposed the methods to improve its performance based on the measurement results. The correlation coefficient between fluctuations of the magnetic field generated by coils and the spin Larmor precession frequency is 0.97, which mainly dominates the stability in a short term. The accuracy of the magnetometer is affected by the power and frequency of the pump light. The Larmor precession frequency coefficient related to the pump light power is 26 mHz/mW, and the effect on the Larmor precession frequency is minimized when the pump light frequency is red detuned by 200 MHz from the 85Rb transition D1 line F = 3 to F′ = 3. The 1/τ measurement time after these corrections can be extended to 10 s, and the sensitivity achieved is 149 fT/Hz, which is close to the quantum projection noise limit of the system.

Second-Scale Coherence Measured at the Quantum Projection Noise Limit with Hundreds of Molecular Ions.

Cold molecules provide an excellent platform for quantum information, cold chemistry, and precision measurement. Certain molecules have enhanced sensitivity to beyond standard model physics, such as the electron's electric dipole moment (eEDM). Molecular ions are easily trappable and are therefore particularly attractive for precision measurements where sensitivity scales with interrogation time. Here, we demonstrate a spin precession measurement with second-scale coherence at the quantum projection noise (QPN) limit with hundreds of trapped molecular ions, chosen for their sensitivity to the eEDM rather than their amenability to state control and readout. Orientation-resolved resonant photodissociation allows us to simultaneously measure two quantum states with opposite eEDM sensitivity, reaching the QPN limit and fully exploiting the high count rate and long coherence.

Towards a compact, optically interrogated, cold-atom microwave clock

Abstract A compact platform for cold atoms opens a range of exciting possibilities for portable, robust and accessible quantum sensors. In this work, we report on the development of a cold-atom microwave clock in a small package. Our work utilises the grating magneto-optical trap and high-contrast coherent population trapping in the lin ⊥ $\perp $ lin polarisation scheme. We optically probe the atomic ground-state splitting of cold 87Rb atoms using a Ramsey-like sequence whilst the atoms are in free-fall. We have measured a short-term fractional frequency stability of 5 × 10 − 11 / τ $5{\times}{10}^{-11}/\sqrt{\tau }$ with a projected quantum projection noise limit at the 10 − 13 / τ ${10}^{-13}/\sqrt{\tau }$ level.

Improved Test of Local Lorentz Invariance from a Deterministic Preparation of Entangled States.

The high degree of control available over individual atoms enables precision tests of fundamental physical concepts. In this Letter, we experimentally study how precision measurements can be improved by preparing entangled states immune to the dominant source of decoherence. Using ^{40}Ca^{+} ions, we explicitly demonstrate the advantage from entanglement on a precision test of local Lorentz invariance for the electron. Reaching the quantum projection noise limit set by quantum mechanics, we observe, for bipartite entangled states, the expected gain of a factor of two in the precision. Under specific conditions, multipartite entangled states may yield substantial further improvements. Our measurements improve the previous best limit for local Lorentz invariance of the electron using ^{40}Ca^{+} ions by a factor of two to four to about 5×10^{-19}.

Drift-Compensated Low-Noise Frequency Synthesis Based on a cryoCSO for the KRISS-F1

In this paper, we report on the implementation and stability analysis of a drift-compensated frequency synthesizer from a cryogenic sapphire oscillator (CSO) designed for a Cs/Rb atomic fountain clock. The synthesizer has two microwave outputs of 7 and 9 GHz for Rb and Cs atom interrogation, respectively. The short-term stability of these microwave signals, measured using an optical frequency comb locked to an ultrastable laser, is better than $5 \times 10^{-15}$ at an averaging time of 1 s. We demonstrate that the short-term stability of the synthesizer is lower than the quantum projection noise limit of the Cs fountain clock, KRISS-F1(Cs) by measuring the short-term stability of the fountain with varying trapped atom number. The stability of the atomic fountain at 1 s averaging time reaches $2.5 \times 10^{-14}$ at the highest atom number in the experiment when the synthesizer is used as an interrogation oscillator of the fountain. In order to compensate the frequency drift of the CSO, the output frequency of a waveform generator, in the synthesis chain, is ramped linearly. By doing this, the frequency stability of the synthesizer at an average time of one hour reaches a level of $10^{-16}$ , which is measured with the fountain clock.

Differential phase extraction in an atom gradiometer

We present here a method for the extraction of the differential phase of an atom gradiometer that exploits the correlation of the vibration signal measured by an auxiliary classical sensor, such as a seismometer or an accelerometer. We show that sensitivities close to the quantum projection noise limit can be reached, even when the vibration noise induces phase fluctuations larger than $2\ensuremath{\pi}$. This method does not require the correlation between the atomic and classical signals to be perfect and allows for an exact determination of the differential phase, with no bias. It can also be applied to other configurations of differential interferometers, such as gyrometers, conjugate interferometers for the measurement of the fine-structure constant, or differential accelerometers for tests of the equivalence principle or detection of gravitational waves.

Frequency noise processes in a strontium ion optical clock

A recent comparison of the frequencies of a pair of optical clocks based on the 674 nm 2S1/2–2D5/2 optical clock transition in 88Sr+ has highlighted the need to understand factors affecting frequency instability. We have developed statistical models to show that our clock is capable of reaching the quantum projection noise limit; for our clock using 100 ms probe pulses, this is ∼3 × 10−15/√τ. However, this optical clock uses atomic transitions with a linear Zeeman shift, which can lead to a degradation in stability in the presence of magnetic field noise. We show that this generally leads to an increase in white frequency noise, even in cases dominated by magnetic field flicker or random walk noise. By taking into account both the quantum projection and magnetic field noise we are able to explain our observed frequency instabilities. This analysis will relate to any optical clock with a linear Zeeman shift where cancellation of this shift is achieved by interrogating pairs of components. Furthermore, implementing automatic control of lasers and minimization of micromotion requires pausing of the frequency servo occasionally; this leads to only a small degradation of frequency stability.

Reducing collective quantum state rotation errors with reversible dephasing

We demonstrate that reversible dephasing via inhomogeneous broadening can greatly reduce collective quantum state rotation errors, and observe the suppression of rotation errors by more than 21 dB in the context of collective population measurements of the spin states of an ensemble of 2.1×105 laser cooled and trapped 87Rb atoms. The large reduction in rotation noise enables direct resolution of spin state populations 13(1) dB below the fundamental quantum projection noise limit. Further, the spin state measurement projects the system into an entangled state with 9.5(5) dB of directly observed spectroscopic enhancement (squeezing) relative to the standard quantum limit, whereas no enhancement would have been obtained without the suppression of rotation errors.

Atomic fountain clock with very high frequency stability employing a pulse-tube-cryocooled sapphire oscillator.

The frequency stability of an atomic fountain clock was significantly improved by employing an ultra-stable local oscillator and increasing the number of atoms detected after the Ramsey interrogation, resulting in a measured Allan deviation of 8.3 × 10(-14)τ(-1/2)). A cryogenic sapphire oscillator using an ultra-low-vibration pulse-tube cryocooler and cryostat, without the need for refilling with liquid helium, was applied as a local oscillator and a frequency reference. High atom number was achieved by the high power of the cooling laser beams and optical pumping to the Zeeman sublevel m(F) = 0 employed for a frequency measurement, although vapor-loaded optical molasses with the simple (001) configuration was used for the atomic fountain clock. The resulting stability is not limited by the Dick effect as it is when a BVA quartz oscillator is used as the local oscillator. The stability reached the quantum projection noise limit to within 11%. Using a combination of a cryocooled sapphire oscillator and techniques to enhance the atom number, the frequency stability of any atomic fountain clock, already established as primary frequency standard, may be improved without opening its vacuum chamber.

Accelerating the averaging rate of atomic ensemble clock stability using atomic phase lock

We experimentally demonstrated that the stability of an atomic clock improves at its fastest rate τ−1 (where τ is the averaging time) when the phase of a local oscillator is genuinely compared to the continuous phase of many atoms in a single trap (an atomic phase lock). For this demonstration, we developed a simple method that repeatedly monitors the atomic phase while retaining its coherence by observing only a portion of the whole ion cloud. Using this new method, we measured the continuous phase over three measurement cycles, and thereby improved the stability scaling from to τ−1 during the three measurement cycles. This simple method provides a path by which atomic clocks can approach a quantum projection noise limit, even when the measurement noise is dominated by the technical noise.

Comparison of Two Independent Sr Optical Clocks with1×10−17Stability at103 s

Many-particle optical lattice clocks have the potential for unprecedented measurement precision and stability due to their low quantum projection noise. However, this potential has so far never been realized because clock stability has been limited by frequency noise of optical local oscillators. By synchronously probing two ^{87}Sr lattice systems using a laser with a thermal noise floor of 1×10(-15), we remove classically correlated laser noise from the intercomparison, but this does not demonstrate independent clock performance. With an improved optical oscillator that has a 1×10(-16) thermal noise floor, we demonstrate an order of magnitude improvement over the best reported stability of any independent clock, achieving a fractional instability of 1×10(-17) in 1000 s of averaging time for synchronous or asynchronous comparisons. This result is within a factor of 2 of the combined quantum projection noise limit for a 160 ms probe time with ~10(3) atoms in each clock. We further demonstrate that even at this high precision, the overall systematic uncertainty of our clock is not limited by atomic interactions. For the second Sr clock, which has a cavity-enhanced lattice, the atomic-density-dependent frequency shift is evaluated to be -3.11×10(-17) with an uncertainty of 8.2×10(-19).

Collective State Measurement of Mesoscopic Ensembles with Single-Atom Resolution

We demonstrate single-atom resolution, as well as detection sensitivity more than 20 dB below the quantum projection noise limit, for hyperfine-state-selective measurements on mesoscopic ensembles containing 100 or more atoms. The measurement detects the atom-induced shift of the resonance frequency of an optical cavity containing the ensemble. While spatially varying coupling of atoms to the cavity prevents the direct observation of a quantized signal, the demonstrated measurement resolution provides the readout capability necessary for atomic interferometry substantially below the standard quantum limit and down to the Heisenberg limit.

Quantum-projection-noise-limited interferometry with coherent atoms in a Ramsey-type setup

Every measurement of the population in an uncorrelated ensemble of two-level systems is limited by what is known as the quantum projection noise limit. Here, we present quantum-projection-noise-limited performance of a Ramsey-type interferometer using freely propagating coherent atoms. The experimental setup is based on an electro-optic modulator in an inherently stable Sagnac interferometer, optically coupling the two interfering atomic states via a two-photon Raman transition. Going beyond the quantum projection noise limit requires the use of reduced quantum uncertainty (squeezed) states. The experiment described demonstrates atom interferometry at the fundamental noise level and allows the observation of possible squeezing effects in an atom laser, potentially leading to improved sensitivity in atom interferometers.