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arXiv:1707.01809 · Optica

Entangled coherent states created by mixing squeezed vacuum and coherent light

Yonatan Israel, Lior Cohen, Xin-Bing Song, Jaewoo Joo, H. S. Eisenberg, Yaron Silberberg

Published May 29, 2019• 32 citations
arXivHTMLPDF

Abstract

Entangled coherent states are shown to emerge, with high fidelity, when mixing coherent and squeezed vacuum states of light on a beam-splitter. These maximally entangled states, where photons bunch at the exit of a beamsplitter, are measured experimentally by Fock-state projections. Entanglement is examined theoretically using a Bell-type nonlocality test and compared with ideal entangled coherent states. We experimentally show nearly perfect similarity with entangled coherent states for an optimal ratio of coherent and squeezed vacuum light. In our scheme, entangled coherent states are generated deterministically with small amplitudes, which could be beneficial, for example, in deterministic distribution of entanglement over long distances.

DOI
10.1364/optica.6.000753

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Entangled coherent states are shown to emerge, with high fidelity, when mixing coherent and squeezed vacuum states of light on a beam-splitter. These maximally entangled states, where photons bunch at the exit of a beamsplitter, are measured experimentally by Fock-state projections. Entanglement is examined theoretically using a Bell-type nonlocality test and compared with ideal entangled coherent states. We experimentally show nearly perfect similarity with entangled coherent states for an optimal ratio of coherent and squeezed vacuum light. In our scheme, entangled coherent states are generated deterministically with small amplitudes, which could be beneficial, for example, in deterministic distribution of entanglement over long distances.
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In the two-cascade-placed beam splitter system, controllable entangled states can be conditionally generated with one squeezed light and two coherent lights. By measuring one photon in one of three output ports, an entangled quantum state can be generated in the remaining two ports. Using the Schmidt decomposition technique, we calculate the degree of entanglement, and maximize the degree of entanglement by adjusting the three input beams and the transmittances of the two beam splitters. The degree of entanglement can be easily adjusted by changing the relative phase angle of the input states.
The numerical conditions to generate high-purity |1 >, |2 >, and |1 > + re iψ |2 > states were found from the explicit form of the probability amplitudes for two cascade-placed beam splitters with one squeezed state input and two coherent state inputs. The expected theoretical signal-tonoise ratio is more than 1000. Controlling the amplitudes and the phases of two coherent beams, as well as the transmittances of two beam splitters, allow various quantum states to be manipulated with a high signal-to-noise ratio. High-purity nonclassical states are expected to be a key element in quantum information science.
Beam splitters are routinely used for generating entanglement between modes in the optical and microwave domains, requiring input states that are not convex combinations of coherent states. This leads to the ability to generate entanglement at a beam splitter as a notion of quantumness. A similar, yet distinct, notion of quantumness is the amount of entanglement generated by two-mode squeezers (i.e., four-wave mixers). We show that squeezed-vacuum states, paradoxically, both minimize and maximize these notions of quantumness, with the crucial resolution of the paradox hinging upon the relative phases between the input states and the devices. Our notion of quantumness is intrinsically related to eigenvalue equations involving creation and annihilation operators, governed by a set of inequalities that leads to generalized cat and squeezed-vacuum states.
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We investigate coherent perfect absorption (CPA) of squeezed coherent states of light by an absorbing beam splitter. First we derive the absorption coefficients for quantum coherence and for intensity, which generally differ. Secondly, we present the remarkable properties of a CPA-gate: two identical but otherwise arbitrary incoming squeezed coherent states can be completely stripped off their coherence, producing a pure entangled squeezed vacuum state at the output. Importantly, this output state of light is not entangled with the absorbing beam splitter by which it was produced. This makes the CPA gate potentially interesting for continuous-variable quantum state preparation.