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Register a new userThe phase sensitivity of a fully quantum three-mode nonlinear interferometer
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Added by
Jefferson Fl\\'orez
Publication date
2018
fields
Physics
and research's language is
English
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We study a nonlinear interferometer consisting of two consecutive parametric amplifiers, where all three optical fields (pump, signal and idler) are treated quantum mechanically, allowing for pump depletion and other quantum phenomena. The interaction of all three fields in the final amplifier leads to an interference pattern from which we extract the phase uncertainty. We find that the phase uncertainty oscillates around a saturation level that decreases as the mean number $N$ of input pump photons increases. For optimal interaction strengths, we also find a phase uncertainty below the shot-noise level and obtain a Heisenberg scaling $1/N$. This is in contrast to the conventional treatment within the parametric approximation, where the Heisenberg scaling is observed as a function of the number of down-converted photons inside the interferometer.
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SU(1,1) interferometers, based on the usage of nonlinear elements, are superior to passive interferometers in phase sensitivity. However, the SU(1,1) interferometer cannot make full use of photons carrying phase information as the second nonlinear element annihilates some of the photons inside. Here, we focus on improving phase sensitivity and propose a new protocol based on a modified SU(1,1) interferometer, where the second nonlinear element is replaced by a beam splitter. We utilize two coherent states as inputs and implement balanced homodyne measurement at the output. Our analysis suggests that the protocol we propose can achieve sub-shot-noise-limited phase sensitivity and is robust against photon loss and background noise. Our work is important for practical quantum metrology using SU(1,1) interferometers.
We theoretically study the phase sensitivity of the SU(1,1) interferometer with a coherent light together with a squeezed vacuum input case using the method of homodyne. We find that the homodyne detection has better sensitivity than the intensity detection under this input case. For a certain intensity of coherent light (squeezed light) input, the relative phase sensitivity is not always better with increasing the squeezed strength (coherent light strength). The phase sensitivity can reach the Heisenberg limit only under a certain moderate parameter interval, which can be realized with current experiment ability.
The phase uncertainty of an unseeded nonlinear interferometer, where the output of one nonlinear crystal is transmitted to the input of a second crystal that analyzes it, is commonly said to be below the shot-noise level but highly dependent on detection and internal loss. Unbalancing the gains of the first (source) and second (analyzer) crystals leads to a configuration that is tolerant against detection loss. However, in terms of sensitivity, there is no advantage in choosing a stronger analyzer over a stronger source, and hence the comparison to a shot-noise level is not straightforward. Internal loss breaks this symmetry and shows that it is crucial whether the source or analyzer is dominating. Based on these results, claiming a Heisenberg scaling of the sensitivity is more subtle than in a balanced setup.
Control over the spectral properties of the bright squeezed vacuum (BSV), a highly multimode non-classical macroscopic state of light that can be generated through high-gain parametric down conversion, is crucial for many applications. In particular, in several recent experiments BSV is generated in a strongly pumped SU(1,1) interferometer to achieve phase supersensitivity, perform broadband homodyne detection, or tailor the frequency spectrum of squeezed light. In this work, we present an analytical approach to the theoretical description of BSV in the frequency domain based on the Bloch-Messiah reduction and the Schmidt-mode formalism. As a special case we consider a strongly pumped SU(1,1) interferometer. We show that different moments of the radiation at its output depend on the phase, dispersion and the parametric gain in a nontrivial way, thereby providing additional insights on the capabilities of nonlinear interferometers. In particular, a dramatic change in the spectrum occurs as the parametric gain increases.
The theory of phase control of coherence, entanglement and quantum steering is developed for an optomechanical system composed of a single mode cavity containing a partially transmitting dielectric membrane and driven by short laser pulses. The closed loop in the coupling creates interfering channels which depend on the relative phase of the coupling strengths of the field modes to the mechanical mode. We show several interesting phase dependent effects such as reversible population transfer from one field mode to the other, creation of collective modes, and induced coherence without induced emission. These effects result from perfect mutual coherence between the field modes which is preserved even if one of the modes is not populated. Depending on the phase, the field modes can act on the mechanical mode collectively or individually resulting, respectively, in tripartite or bipartite entanglement. In addition, we examine the phase sensitivity of quantum steering of the mechanical mode by the field modes is investigated. Deterministic phase transfer of the steering from bipartite to collective is predicted and optimum steering corresponding to perfect EPR state can be achieved. These different types of quantum steering can be distinguished experimentally by measuring the coincidence rate between two detectors adjusted to collect photons of the output cavity modes. In particular, we find that the minima of the interference pattern of the coincidence rate signal the bipartite steering, while the maxima signal the collective steering.
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