Improving Quantum Clocks via Semidefinite Programming | NIST

Emanuel H. Knill

MICHAEL J. MULLAN, Emanuel H. Knill

The accuracies of modern quantum logic clocks have surpassed those of standard atomic fountain clocks. These clocks also provide a greater degree of control, because before and after clock queries, we are able to apply chosen unitary operations and measurements. Here, we take advantage of these choices and present a numerical technique designed to increase the accuracy of these clocks. We use a greedy approach, minimizing the phase variance of a noisy classical oscillator with respect to a perfect frequency standard after an interrogation step; we do not optimize over successive interrogations or the probe times. We consider arbitrary prior frequency knowledge and compare clocks with varying numbers of ions and queries interlaced with unitary control. Our technique is based on the semidefinite programming formulation of quantum query complexity, a method first developed in the context of deriving algorithmic lower bounds. The application of semidefinite programming to an inherently continuous problem like that considered here requires discretization; we derive bounds on the error introduced and show that it can be made suitably small.

Till Rosenband

MICHAEL J. MULLAN, Emanuel H. Knill

The accuracies of modern quantum logic clocks have surpassed those of standard atomic fountain clocks. These clocks also provide a greater degree of control, because before and after clock queries, we are able to apply chosen unitary operations and measurements. Here, we take advantage of these choices and present a numerical technique designed to increase the accuracy of these clocks. We use a greedy approach, minimizing the phase variance of a noisy classical oscillator with respect to a perfect frequency standard after an interrogation step; we do not optimize over successive interrogations or the probe times. We consider arbitrary prior frequency knowledge and compare clocks with varying numbers of ions and queries interlaced with unitary control. Our technique is based on the semidefinite programming formulation of quantum query complexity, a method first developed in the context of deriving algorithmic lower bounds. The application of semidefinite programming to an inherently continuous problem like that considered here requires discretization; we derive bounds on the error introduced and show that it can be made suitably small.

John Chiaverini, Dietrich G. Leibfried, Tobias Schaetz +9 more

MICHAEL J. MULLAN

We describe quantum interrogation schemes for passive atomic clocks. During any given interrogation period, the optimal interrogation algorithm depends on the state of the clock -- specifically on the frequency deviation of the flywheel (classical oscillator) from the atomic standard. As a clock runs, it is possible to estimate this deviation. Nonetheless, traditional schemes use the same, fixed algorithm for each interrogation period, which is necessarily independent of this prior knowledge. Here we present a dynamic scheme, tailoring our algorithms to the clock's state before each interrogation. These strategies are derived by constructing a complete model of a passive clock -- specifically, a probability distribution describing the estimated average offset frequency of the flywheel during both the upcoming interrogation period and interrogation periods in the past is updated via appropriate noise models and by measurements of the atomic standard.\nTo reduce the deviation from an ideal clock we optimize the next interrogation algorithm by means of a semidefinite program for atomic state preparation and measurement whose objective function depends on the updated state. This program is based on the semidefinite programming formulation of quantum query complexity, a method first developed in the context of deriving algorithmic lower bounds. The application of semidefinite programming to an inherently continuous problem like that considered here requires discretization; we derive bounds on the error introduced and show that it can be made suitably small.\nFinally, we implement a full simulation of a passive clock with power-law noise models and find significant improvements by applying our techniques.