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Register a new userApproaching the Heisenberg limit in an atom laser
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We present experimental and theoretical results showing the improved beam quality and reduced divergence of an atom laser produced by an optical Raman transition, compared to one produced by an RF transition. We show that Raman outcoupling can eliminate the diverging lens effect that the condensate has on the outcoupled atoms. This substantially improves the beam quality of the atom laser, and the improvement may be greater than a factor of ten for experiments with tight trapping potentials. We show that Raman outcoupling can produce atom lasers whose quality is only limited by the wavefunction shape of the condensate that produces them, typically a factor of 1.3 above the Heisenberg limit.
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We propose an approach to quantum phase estimation that can attain precision near the Heisenberg limit without requiring single-particle-resolved state detection. We show that the one-axis twisting interaction, well known for generating spin squeezing in atomic ensembles, can also amplify the output signal of an entanglement-enhanced interferometer to facilitate readout. Applying this interaction-based readout to oversqueezed, non-Gaussian states yields a Heisenberg scaling in phase sensitivity, which persists in the presence of detection noise as large as the quantum projection noise of an unentangled ensemble. Even in dissipative implementations -- e.g., employing light-mediated interactions in an optical cavity or Rydberg dressing -- the method significantly relaxes the detection resolution required for spectroscopy beyond the standard quantum limit.
We consider the interaction of atomic hydrogen, in its ground state, with an electromagnetic pulse whose duration is fixed in terms of the number of optical cycles. We study the probability of excitation of the atom in the static field limit i.e. for field frequencies going to zero. Despite the fact that the well known Born-Fock adiabatic theorem is valid only for a system whose energy spectrum is discrete, we show that it is still possible to use this theorem to derive, in the low frequency limit, an analytical formula which gives the probability of transition to any excited state of the atom as a function of the field intensity, the carrier envelope phase and the number of optical cycles within the pulse. The results for the probability of excitation to low-lying excited states, obtained with this formula, agree with those we get by solving the time-dependent Schroedinger equation. The domain of validity is discussed in detail.
The use of quantum resources can provide measurement precision beyond the shot-noise limit (SNL). The task of ab initio optical phase measurement---the estimation of a completely unknown phase---has been experimentally demonstrated with precision beyond the SNL, and even scaling like the ultimate bound, the Heisenberg limit (HL), but with an overhead factor. However, existing approaches have not been able---even in principle---to achieve the best possible precision, saturating the HL exactly. Here we demonstrate a scheme to achieve true HL phase measurement, using a combination of three techniques: entanglement, multiple samplings of the phase shift, and adaptive measurement. Our experimental demonstration of the scheme uses two photonic qubits, one double passed, so that, for a successful coincidence detection, the number of photon-passes is $N=3$. We achieve a precision that is within $4%$ of the HL, surpassing the best precision theoretically achievable with simpler techniques with $N=3$. This work represents a fundamental achievement of the ultimate limits of metrology, and the scheme can be extended to higher $N$ and other physical systems.
To quantify quantum optical coherence requires both the particle- and wave-natures of light. For an ideal laser beam [1,2,3], it can be thought of roughly as the number of photons emitted consecutively into the beam with the same phase. This number, $mathfrak{C}$, can be much larger than $mu$, the number of photons in the laser itself. The limit on $mathfrak{C}$ for an ideal laser was thought to be of order $mu^2$ [4,5]. Here, assuming nothing about the laser operation, only that it produces a beam with certain properties close to those of an ideal laser beam, and that it does not have external sources of coherence, we derive an upper bound: $mathfrak{C} = O(mu^4)$. Moreover, using the matrix product states (MPSs) method [6,7,8,9], we find a model that achieves this scaling, and show that it could in principle be realised using circuit quantum electrodynamics (QED) [10]. Thus $mathfrak{C} = O(mu^2)$ is only a standard quantum limit (SQL); the ultimate quantum limit, or Heisenberg limit, is quadratically better.
We describe a scheme, operating in a manner analogous to a reversed Raman output coupler, for measuring the phase-sensitive quadrature statistics of an atom laser beam. This scheme allows for the transferral of the atomic field statistics to an optical field, for which the quantum statistics may then be measured using the well-developed technology of optical homodyne measurement.
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