Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Three-mode squeezing: SU(1,1) symmetry

Zahra Shaterzadeh‐Yazdi, Peter S. Turner, Barry C. Sanders

Published Jun 7, 2007• 2 citations

Abstract

Three-mode (tripartite) squeezed light is important for continuous variable quantum information tasks such as quantum teleportation, state sharing, and generating tripartite continuous variable entangled states, and furthermore is the first nontrivial step towards multipartite squeezed states. In such cases just one two-mode squeezer is used, and the squeezed light is distributed across multiple channels by passive optical elements. Here we show that these three-mode squeezed states are produced by optical networks that can be described as SU(1, 1) transformations, which enables relatively straightforward and elegant calculations of any output state from such squeezing networks for any input state.

DOI: 10.1117/12.724380

Related papers

SU(1,1) symmetry of multimode squeezed states

Zahra Shaterzadeh‐Yazdi, P S Turner, Barry C. Sanders

We show that a class of multimode optical transformations that employ linear optics plus two-mode squeezing can be expressed as SU(1,1) operators. These operations are relevant to state-of-the-art continuous variable quantum information experiments including quantum state sharing, quantum teleportation and multipartite entangled states. Using this SU(1,1) description of these transformations, we obtain a new basis for such transformations that lies in a useful representation of this group and lies outside the often-used restriction to Gaussian states. We analyze this basis, show its application to a class of transformations and discuss its extension to more general quantum optical networks.

arXiv:0710.3205Journal of Physics A Mathematical and TheoreticalJan 23, 200822 citations

Multimode squeezed light and coupled squeezed vacuum (Conference Presentation)

Ryan T. Glasser, Wenlei Zhang, Erin M. Knutson +3 more

Multipartite entanglement is a key resource for various quantum information tasks. Here, we present multiple schemes for multimode entanglement and squeezing via nonlinear optical processes. We define a new "coupled three-mode squeezed vacuum" state. Non-intuitive behaviors arise in intensity squeezing between two of the three output modes due to the coupling. We also show that this state can be genuinely tripartite entangled, and extend the work to a four-mode output system.

Optical and Quantum Sensing and Precision Metrology IIMar 9, 20200 citations

Three-mode Gaussian states in quantum information with continuous variables

Gerardo Adesso, Alessio Serafini, Fabrizio Illuminati

The structural aspects of tripartite entanglement in three-mode Gaussian states of continuous variable systems have been studied in [Adesso G, Serafini A and Illuminati F 2006 Phys. Rev. A {\\bf 73} 032345]. Here we focus our attention on the usefulness of such states in the context of realistic processing of continuous-variable quantum information. We introduce and discuss in detail several examples of pure and mixed three-mode states that stand out for their informational and/or entanglement properties. We then describe practical schemes to engineer such states with linear optics. In particular, we introduce a simple procedure -- based on passive optical elements -- to produce pure three-mode Gaussian states with {\\em arbitrary} entanglement structure (upon availability of an initial single-mode squeezed state). We analyze in detail the properties of distributed entanglement, showing that the promiscuity of entanglement sharing is a feature peculiar to symmetric Gaussian states that survives even in the presence of significant degrees of mixedness and decoherence. Next, we discuss the suitability of the considered tripartite entangled states to the implementation of quantum information and communication protocols with continuous variables. This will lead to a feasible experimental proposal to test the promiscuous sharing of continuous-variable entanglement, in terms of the optimal fidelity of teleportation networks with Gaussian resources. As a byproduct, optimal resource states for various communication protocols (among which asymmetric telecloning) will be exactly determined.

Sep 9, 20061 citation

Coupled Three-Mode Squeezed Vacuum

Wenlei Zhang, Ryan T. Glasser

Multipartite entanglement is a key resource for various quantum information tasks. Here, we present a scheme for generating genuine tripartite entanglement via nonlinear optical processes. We derive, in the Fock basis, the corresponding output state which we termed the coupled three-mode squeezed vacuum. We find unintuitive behaviors arise in intensity squeezing between two of the three output modes due to the coupling present. We also show that this state can be genuinely tripartite entangled.

arXiv:2002.00323Feb 2, 20202 citations

Single-mode input squeezing and tripartite entanglement in three-mode ponderomotive optomechanics simulations

Kahlil Dixon, Lior Cohen, Narayan Bhusal +3 more

Quantum entanglement is a crucial resource for a wide variety of quantum technologies. However, the current state-of-art methods to generate quantum entanglement in optomechanical systems are not as efficient as all-optical methods utilizing nonlinear crystals. This article proposes a new scheme in which two single-mode squeezed light fields are injected into an optomechanical cavity. We demonstrate through our numerical simulations that the quantum entanglement can be substantially enhanced with the careful selection of squeezing strength and squeezing angle of the two quadrature squeezed light fields. Our results represent a significant improvement in output bipartite photon-photon entanglement over the previously demonstrated schemes using two coherent light fields as inputs. These simulations predict a maximum increase in bipartite optical entanglement by a factor of about 6, as well as increases in the quantum noise of the output light. A perceived loss of quantum information at certain squeezing angles is attributed to tripartite entanglement between the two optical fields and the optomechanical oscillator (OMO). At particular squeezing angles, the bipartite (or tripartite) entanglement can be increased, thus introducing a method of optically controlling the intracavity entanglement. These mechanics can benefit various optical quantum technologies utilizing optomechanical entanglement and continuous variable quantum optics.

arXiv:2107.07053Jul 15, 20210 citations

New Three—Mode Einstein—Podolsky—Rosen Entangled State Prepresentation and Its Application in Squeezing Theory

范洪义, 姜年权

By extending the Einstein-Podolsky-Rosen bipartite entanglement to the tripartite case,we construct the common eigenvector of the tripartite centre-of -mass coordinate and two mass-weighted relative momenta,which is a new entangled state of continuum variables.The classical dilation transform of varibles in such a state induces new entangled state of continum variables,The classical dilation transform of variables in such a state induces a new three-mode squeezing operator related to a three-mode bosonic operator realization of SU(1,1) Lie algebra.a new three-mode squeezing operator related to a three-mode bosonic operator realization of SU(1,1) Lie algebra.

Chinese Physics LettersJan 1, 20020 citations