We perform a self-synchronous clock comparison between two spin-squeezed ensembles in a strontium optical lattice clock to directly measure 2.0(3) dB of metrological gain beyond quantum projection noise-limited operation, averaging down to the 10 − 17 level.
Building scalable quantum systems that demonstrate genuine performance enhancement based on entanglement is a major scientific goal for fields including computing, networking, simulations, and metrology. The tremendous challenge arises from the fragility of entanglement in increasingly larger sized quantum systems. Optical atomic clocks utilizing a large number of atoms have pushed the frontier of measurement science, building on precise engineering of quantum states and control of atomic interactions. However, today's state-of-the-art optical atomic clocks are limited by the quantum projection noise (QPN) defined by many uncorrelated atoms. Pioneering work on producing spin squeezed states of atoms has shown a path towards integrating entanglement into the best performing clocks. However, to directly demonstrate advantage of quantum entanglement in a working clock we must prevent backaction effects that degrade quantum coherence and introduce uncontrolled perturbations, as well as minimize the influence of technical noise arising from the interrogating clock laser. Here we present a new optical clock platform integrated with collective strong-coupling cavity QED for quantum non-demolition (QND) measurement. Optimizing the competition between spin measurement precision and loss of coherence, we measure a Wineland parameter of -1.8(7) dB for 1.9x104 atoms, thus verifying the presence of entanglement. Furthermore, a moving lattice allows the cavity to individually address two independent sub-ensembles, enabling us to spin squeeze two clock ensembles successively and compare their performance. This differential comparison between the two squeezed clocks directly verifies enhanced clock stability of 2.0(3) dB below QPN, and 0.6(3) dB above the standard quantum limit (SQL), at the measurement precision level of 10−17, without subtracting any technical noise contributions.
High-bandwidth, high-stability clocks offer unique chances to study fundamental physics beyond simple metrology. Today, the most stable clocks are optical lattice clocks and they can reach a fractional stability of 3.1 × 10^−18 at 1 s averaging time. Their applications are ranging from the redefinition of the SI time unit, the Second, to the possible detection of gravitational waves in space. The stability of optical lattice clocks is primarily limited by quantum projection noise and Dick noise. In this thesis, I present our effort in creating a platform for studying quantum enhanced metrology and its application towards optical lattice clocks. We demonstrated the laser cooling in an optical cavity with Raman-sideband cooling and achieved average vibration number of n = 0.2. We utilized cavity feedback squeezing to demonstrate unitary spin squeezing on magnetic sub-levels of 171Yb, achieving 6.5 dB quantum projection noise reduction over the standard quantum limit (SQL). With coherent optical state transfer by ultra stable laser pulses, we successfully transferred the spin squeezed state from magnetic sub-levels to the optical transition, and demonstrated quantum enhanced metrology in the optical lattice clock for the first time. We achieved 4.4 dB of metrological gain over the SQL, which corresponds to a reduction of the averaging time by a factor of 2.8 in clock operation. Furthermore, we studied quantum enhanced metrology with time-reversal-based protocols. We performed a signal amplification through time-reversed interaction protocol between the ground state magnetic sublevels of 171Yb, achieving the largest sensitivity improvement beyond SQL in any interferometers to date at 11.8dB. Besides that, we experimentally studied the connection between quantum information scrambling, by measuring out-of-time-order correlators (OTOCs), and quantum metrology, by measuring metrological gain. We found these values to agree with each other, and concluded that the time-reversal quantum metrology can saturate the attainable gain from the quantum information scrambling.
Optical atomic clocks with unrivaled precision and accuracy have advanced the frontier of precision measurement science and opened new avenues for exploring fundamental physics. A fundamental limitation on clock precision is the standard quantum limit (SQL), which stems from the uncorrelated projection noise of each atom. State-of-the-art optical lattice clocks interrogate large ensembles to minimize the SQL, but density-dependent frequency shifts pose challenges to scaling the atom number. The SQL can be surpassed, however, by leveraging entanglement, though it remains an open problem to achieve quantum advantage from spin squeezing at state-of-the-art stability levels. Here, we demonstrate clock performance beyond the SQL, achieving a fractional frequency precision of 1.1×10^{-18} for a single spin-squeezed clock. With cavity-based quantum nondemolition measurements, we prepare two spin-squeezed ensembles of ∼30 000 strontium atoms confined in a two-dimensional optical lattice. A synchronous clock comparison with an interrogation time of 61 ms achieves a metrological improvement of 2.0(2) dB beyond the SQL, after correcting for state preparation and measurement errors. These results establish the most precise entanglement-enhanced clock to date and offer a powerful platform for exploring the interplay of gravity and quantum entanglement.
Optical atomic clocks utilizing strontium are the gold standard of timekeeping. Generating entanglement by spin-squeezing has the potential to continue pushing the limits of clock stability below the fundamental performance limit for unentangled ensembles, the standard quantum limit (SQL). One way to do so is by using an optical cavity to transduce interactions between the atoms and to improve the cavity readout, one needs to minimize the noise of the stabilized cavity length. Noise in a control loop can arise from many different sources, including mechanical resonances of the piezo (PZT) used to control the cavity length, so addressing this noise can improve clock stability and maximize the capabilities of quantum sensing. For this project, I measured the transfer function of the piezo-cavity system, inverted this transfer function, and extracted the poles and zeros. I then programmed this tailored digital filter on a Red Pitaya using an open-source Python package, PyRPL. Challenges still remain with the device implementation into the control loop, but afterwards this would ultimately contribute to improved clock precision and attain better spin-squeezing generated by the cavity.
Many-body entangled states allow precision measurement beyond the standard quantum limit. Yet they have not been effectively exploited in optical lattice clocks except for proof-of-principle demonstrations. Under the current experimental conditions, taking into account the lattice perturbation, atom-atom interactions, and local oscillator noise, we theoretically evaluate the performance of spin-squeezing-based shallow-lattice Yb optical clocks. The numerical simulation shows that the stability of differential frequency comparison between two Yb ensembles in squeezed spin states potentially accesses the ${10}^{\ensuremath{-}19}$ level at the averaging time of 1 s. The resultant Wineland parameter may be as low as ${\ensuremath{\xi}}_{\text{W}}^{2}=0.027$, corresponding to a reduction of averaging time by a factor of 37, and is limited by the collision-induced degradation of spin squeezing. The metrological gain provided by spin squeezing opens up new opportunities for precision measurement and fundamental physics.