We show that two-mode squeezed vacuum-like states may be engineered in the Bohm–Madelung formalism by adequately choosing the phase of the wave function. The difference between our wave function and the one of the squeezed vacuum states is given precisely by the phase we selected. We would like to stress that the engineering of two-mode vacuum states is possible due to the existence of the Bohm potential, and it is relevant because of its potential use in the propagation of optical fields, where it may render a variety of applications in optics. The approach to generate non-classical states, namely, two-mode squeezed states of a quantum mechanical system is one of the first applications of the Madelung–Bohm formalism.
We show that two-mode squeezed vacuum-like states may be engineered in the Bohm–Madelung formalism by adequately choosing the phase of the wave function. The difference between our wave function and the one of the squeezed vacuum states is given precisely by the phase we selected. We would like to stress that the engineering of two-mode vacuum states is possible due to the existence of the Bohm potential, and it is relevant because of its potential use in the propagation of optical fields, where it may render a variety of applications in optics. The approach to generate non-classical states, namely, two-mode squeezed states of a quantum mechanical system is one of the first applications of the Madelung–Bohm formalism.
We propose to generate two-mode squeezed vacuum motional state of an intracavity trapped ion by taking the advantage of the dissipation of the cavity mode. At the first step, the steady and pure two-mode motional entanglement between two motional degrees of the cold ion is obtained by engineering the couplings of both the motional modes of the ion to the cavity field. Based on the first step, a two-mode squeezed vacuum motional state is then generated by manipulating the phases of the external laser pulses incident on the ion.
Decoherence remains one of the most serious challenges to the implementation of quantum technology. It appears as a result of the transformation over time of a quantum superposition state into a classical mixture due to the quantum system interacting with the environment. Since quantum systems are never completely isolated from their environment, decoherence therefore cannot be avoided in realistic situations. Decoherence has been extensively studied, mostly theoretically, because it has many important implications in quantum technology, such as in the fields of quantum information processing, quantum communication, and quantum computation. Here we report a novel experimental scheme on the study of decoherence of a two-mode squeezed vacuum state via its second harmonic generation signal. Our scheme can directly extract the decoherence of the phase-sensitive quantum correlation $\ensuremath{\langle}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{b}\ensuremath{\rangle}$ between two entangled modes a and b. Such a correlation is the most important characteristic of a two-mode squeezed state. More importantly, this is an experimental study on the decoherence effect of a squeezed vacuum state, which has been rarely investigated.
Engineering non-classical states of the electromagnetic field is a central quest for quantum optics1,2. Beyond their fundamental significance, such states are indeed the resources for implementing various protocols, ranging from enhanced metrology to quantum communication and computing. A variety of devices can be used to generate non-classical states, such as single emitters, light-matter interfaces or non-linear systems3. We focus here on the use of a continuous-wave optical parametric oscillator3,4. This system is based on a non-linear χ2 crystal inserted inside an optical cavity and it is now well-known as a very efficient source of non-classical light, such as single-mode or two-mode squeezed vacuum depending on the crystal phase matching. Squeezed vacuum is a Gaussian state as its quadrature distributions follow a Gaussian statistics. However, it has been shown that number of protocols require non-Gaussian states5. Generating directly such states is a difficult task and would require strong χ3 non-linearities. Another procedure, probabilistic but heralded, consists in using a measurement-induced non-linearity via a conditional preparation technique operated on Gaussian states. Here, we detail this generation protocol for two non-Gaussian states, the single-photon state and a superposition of coherent states, using two differently phase-matched parametric oscillators as primary resources. This technique enables achievement of a high fidelity with the targeted state and generation of the state in a well-controlled spatiotemporal mode.
Engineering non-classical states of the electromagnetic field is a central quest for quantum optics(1,2). Beyond their fundamental significance, such states are indeed the resources for implementing various protocols, ranging from enhanced metrology to quantum communication and computing. A variety of devices can be used to generate non-classical states, such as single emitters, light-matter interfaces or non-linear systems(3). We focus here on the use of a continuous-wave optical parametric oscillator(3,4). This system is based on a non-linear χ(2) crystal inserted inside an optical cavity and it is now well-known as a very efficient source of non-classical light, such as single-mode or two-mode squeezed vacuum depending on the crystal phase matching. Squeezed vacuum is a Gaussian state as its quadrature distributions follow a Gaussian statistics. However, it has been shown that number of protocols require non-Gaussian states(5). Generating directly such states is a difficult task and would require strong χ(3) non-linearities. Another procedure, probabilistic but heralded, consists in using a measurement-induced non-linearity via a conditional preparation technique operated on Gaussian states. Here, we detail this generation protocol for two non-Gaussian states, the single-photon state and a superposition of coherent states, using two differently phase-matched parametric oscillators as primary resources. This technique enables achievement of a high fidelity with the targeted state and generation of the state in a well-controlled spatiotemporal mode.
Although the geometric phase for one-mode squeezed state had been studied in detail, the counterpart for two-mode squeezed state is vacant. In this paper, we aim at the special case, namely, two-mode squeezed vacuum state. Furthermore, the total phase factor is to be written in an elegant form, which is just identical to one term of product of two squeezed operators. In addition, when this system undergoes cyclic evolutions, the corresponding geometric phase is obtained, which is the sum of the counterparts of two isolated one-mode squeezed vacuum state. Finally, the relationship between the cyclic geometric phase and entanglement of two-mode squeezed vacuum state is established. Key words: Quantum optics, Geometric phases, Entanglement
Squeezed states of the electromagnetic field are characterized by a reduction of fluctuations for one of two quadrature phase amplitudes below the level of fluctuations for the vacuum state. This reduction is a manifestly quantum or nonclassical feature which is of great interest in its own right but also potentially important for precision measurement with sensitivity beyond the shot-noise or vacuum-state limit. We describe three different experiments in which squeezed light has been generated in our laboratory involving parametric downconversion, intracavity frequency doubling, and optical bistability with two-state atoms. By employing the squeezed light produced by a subthreshold optical parametric oscillator, we have achieved improvements in sensitivity beyond the vacuum-state limit for the detection of both phase and amplitude changes of the electromagnetic field. An alternate route to sensitivity beyond the vacuum-state limit is through quantum nondemolition measurement, where we have suggested and are implementing a scheme involving parametric conversion and polarization mixing.