The precision of an atomic clock based on the standard Ramsey spectroscopy, involving the measurement of the population of the atomic excited state, essentially a measurement of energy, is determined by the free evolution time T between successive /2 pulses. The longer the time T, the narrower the Ramsey interference fringes and thus the greater the precision. The stability of an atomic clock is also increased with increased T. But there are practical limits to the degree to which T can be extended. The main approach so far has been through the introduction of the so-called atomic fountain clocks. In this talk we present alternative approach not based on extending T but based on collective atomic states where a non-classical observable, an observable having no classical counterpart, is to be measured. This is the collective atomic, or SU(2), parity for an ensemble of two-level atoms. We show that with this observable the corresponding Ramsey-like fringes can become remarkably narrower with an increasing number of atoms in the ensemble even when the atomics are not prepared in an entangled state. By preparing the atoms in an entangled state, such as a state known to be spin-squeezed, the precision can be further increased through atomic parity measurements. The issue of performing the required collective atomic parity measurements will be discussed.
The precision of an atomic clock based on the standard Ramsey spectroscopy, involving the measurement of the population of the atomic excited state, essentially a measurement of energy, is determined by the free evolution time T between successive /2 pulses. The longer the time T, the narrower the Ramsey interference fringes and thus the greater the precision. The stability of an atomic clock is also increased with increased T. But there are practical limits to the degree to which T can be extended. The main approach so far has been through the introduction of the so-called atomic fountain clocks. In this talk we present alternative approach not based on extending T but based on collective atomic states where a non-classical observable, an observable having no classical counterpart, is to be measured. This is the collective atomic, or SU(2), parity for an ensemble of two-level atoms. We show that with this observable the corresponding Ramsey-like fringes can become remarkably narrower with an increasing number of atoms in the ensemble even when the atomics are not prepared in an entangled state. By preparing the atoms in an entangled state, such as a state known to be spin-squeezed, the precision can be further increased through atomic parity measurements. The issue of performing the required collective atomic parity measurements will be discussed.
This thesis describes new results on the entanglement of atomic spins in Ramsey interferometry, optical atomic clocks and trapped ions. It is divided into three parts: First, we investigate improvements to conventional Ramsey interferometry with entanglement and adding only rotations of the collective spin to adjust the signal and measurement directions. The geometric degrees of freedom, connected to the rotations, are analytically optimized for a large class of generalized Ramsey protocols to allow efficient optimization of all parameters. Besides a unification of existing approaches, the main result is that there is only one new protocol, where a previously unused double inversion is applied. Studies of the local sensitivity show that this protocol reaches the fundamental quantum Fisher information limit and is yet robust against errors during preparation and measurement. In the second section we investigate the conditions under which optical atomic clocks exhibit increased long-term stability when applying weakly entangled, spin squeezed states. We discuss the common case of an atomic clock with a single ensemble, typical Brownian frequency noise and finite dead time. Theoretical modelling of the servo loop allows quantitative predictions of the optimal stability for given values of dead time and laser noise, in very good agreement with numerical simulations of the closed feedback loop. The main result is that, even with the current most stable lasers, the clock stability can only be improved for ensembles below a critical atom number of about one thousand in optical Sr lattice clocks. Even with a future improvement of the laser performance by one order of magnitude, the critical atom number still remains below 100,000. In contrast, clocks based on smaller, non-scalable ensembles, such as ion clocks, can already benefit from squeezed states with current clock lasers. Thus the last section considers the robust generation of entanglement in ion traps. An error budget including relevant experimental error sources is calculated for state-of-the-art quantum gates, driven by oscillating microwave gradients in surface traps. Amplitude modulation of the driving fields is shown to efficiently counteract the current limitations from motional mode instability. The predicted increase of the gate quality was demonstrated by the group of C. Ospelkaus at PTB Braunschweig, who measured gates with errors as low as ~ 10^(-3). In a similar approach, interactions between spin and motion can also be generated by combining oscillating rf-fields with a static magnetic field gradient. Penning traps designed for precision spectroscopy already feature large magnetic field gradients at the edge of a magnetic bottle configuration. We present parameters and conditions under which laser-free coupling of spin and quantized motion for (anti-)protons is possible at these points, in a step towards quantum logic spectroscopy for (anti-)protons.
Since the pioneering work of Ramsey, atom interferometers are employed for precision metrology, in particular to measure time and to realize the second. In a classical interferometer, an ensemble of atoms is prepared in one of the two input states, whereas the second one is left empty. In this case, the vacuum noise restricts the precision of the interferometer to the standard quantum limit (SQL). Here, we propose and experimentally demonstrate a novel clock configuration that surpasses the SQL by squeezing the vacuum in the empty input state. We create a squeezed vacuum state containing an average of 0.75 atoms to improve the clock sensitivity of 10000 atoms by 2.05_{-0.37}^{+0.34} dB. The SQL poses a significant limitation for today's microwave fountain clocks, which serve as the main time reference. We evaluate the major technical limitations and challenges for devising a next generation of fountain clocks based on atomic squeezed vacuum.
In general, the process of spin squeezing is employed for atomic sensors that are essentially free from the effect of spontaneous emission. In the case of an atomic clock based on coherent population trapping, spontaneous emission plays a key role. Specifically, when the clock is realized in the Ramsey configuration employing a pair of pulses separated in time, it is the spontaneous emission process during the first pulse that creates the coherent population trapping, by optically pumping the atoms into the so-called dark state. We show in this talk that it is still possible to apply the process of spin squeezing to enhance the sensitivity of such a clock, by designing carefully the sequence of steps in the protocol. Specifically, we consider the approach of using the maximally entangled Schroedinger Cat states, produced via one axis twist squeezing, to achieve Heisenberg Limited sensitivity, representing an improvement in sensitivity by as much as four orders of magnitude.
We investigate Ramsey spectroscopy performed on a synchronized ensemble of two-level atoms. The synchronization is induced by the collective coupling of the atoms to a heavily damped mode of an optical cavity. We show that, in principle, with this synchronized system it is possible to observe Ramsey fringes indefinitely, even in the presence of spontaneous emission and other sources of individual-atom dephasing. This could have important consequences for atomic clocks and a wide range of precision metrology applications.
The stability of an optical atomic clock is a critical figure of merit for almost all clock applications. To this end, much optical atomic clock research has focused on reducing clock instability by increasing the atom number, lengthening the coherent interrogation times, and introducing entanglement to push beyond the standard quantum limit. In this work, we experimentally demonstrate an alternative approach to reducing clock instability using a phase estimation approach based on individually controlled atomic ensembles in a strontium (Sr) optical lattice clock. We first demonstrate joint Ramsey interrogation of two spatially resolved atom ensembles that are out of phase with respect to each other, which we call “quadrature Ramsey spectroscopy,” resulting in a factor of 1.36(5) reduction in absolute clock instability as measured with interleaved self-comparisons. We then leverage the rich hyperfine structure of Sr87 to realize independent coherent control over multiple ensembles with only global laser addressing. Finally, we utilize this independent control over four atom ensembles to implement a form of phase estimation, achieving a factor of greater than 3 enhancement in coherent interrogation time and a factor of 2.08(6) reduction in instability over an otherwise identical single-ensemble clock with the same local oscillator and the same number of atoms. We expect that multiensemble protocols similar to those demonstrated here will result in reduction in the instability of any optical lattice clock with an interrogation time limited by the local oscillator. Published by the American Physical Society 2024