Entanglement-assisted atomic clock beyond the projection noise limit

Abstract

Abstract. We use a quantum non-demolition measurement to generate a spin squeezed state and to create entanglement in a cloud of 10 5 cold cesium atoms. For the first time we operate an atomic clock improved by spin squeezing beyond the projection noise limit in a proof-of-principle experiment. For a clockinterrogation time of 10 µs, the experiments show an improvement of 1.1 dB in the signal-to-noise ratio, compared to the atomic projection noise limit.

Quantum metrology for a general Hamiltonian parameter

“…The form of h g in (28) implies that the quantum Fisher information F (Q) g can be divided into two parts: one is due to the dependence of the eigenvalues E k on g, and this part is linear in the time t; the other is due to the dependence of the eigenstates |E (i) k on g, and that part oscillates with time.…”

“…Many applications of quantum metrology have been found, including quantum frequency standards [17,18], optical phase estimation [19][20][21][22][23][24][25], atomic clocks [26][27][28][29][30], atomic interferometers [18,31,32], quantum imaging [32,33], and quantum-enhanced positioning and clock synchronization [34]. The quantum Fisher information has also been studied in open systems [35][36][37][38][39][40][41], along with growing research on protocols assisted by error correction [42][43][44].…”

Unitary cavity spin squeezing by quantum erasure

“…This improvement makes squeezed spin states potentially useful for precision metrology beyond the standard quantum limit (SQL) that is set by the quantum fluctuations of independent particles. In particular, spin squeezing might increase the stability of atomic clocks, magnetometers, and other measurements based on atom interferometry [2][3][4][5]. Many approaches to spin squeezing have been proposed [2,[6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] and a number of them have been demonstrated experimentally, including atomic absorption of squeezed light [22], entangling gates in an ion trap [23], projection by quantum non-demolition (QND) measurement [24][25][26], atom-atom collisions [27][28][29], and lightmediated interaction between distant atoms in an optical resonator [30,31].…”

Heterodyne non-demolition measurements on cold atomic samples: towards the preparation of non-classical states for atom interferometry

“…In that case, the off-resonance modification of the refractive index is measured by the phase shift induced on the probe optical field. Several techniques can be implemented to measure this phase shift, including Mach-Zehnder interferometry [14], mapping phase fluctuations into intensity fluctuations using a cavity tuned on the side of its resonance [11], or comparing the probe dephasing to a far from resonance local oscillator [29,31]. The latter technique, called heterodyne detection, is adopted in the following.…”

“…To go further, the sensitivity can be enhanced by either increasing the number of atoms or reducing the effect of quantum noise [18]. In this context, atomic spin-squeezed states [10] have recently been achieved [3,11], [14][15][16][17], and they have allowed sensitivity enhancement in atomic clocks [11,13,14].…”