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Frontiers in Optics

Generation of Photon-Subtracted Two-Mode Squeezed Vacuum States

Roberto de J. León‐Montiel, Omar S. Magaña‐Loaiza, Armando Pérez-Leija, Alfred B. U’Ren, Kurt Busch, Adriana E. Lita, Sae Woo Nam, Thomas Gerrits, Richard P. Mirin

Published Jan 1, 2018• 1 citation
Publisher

Abstract

We experimentally demonstrate that the simultaneous subtraction of photons from a two-mode squeezed vacuum state leads to the generation of entangled states with increasingly larger average photon number.
DOI
10.1364/ls.2018.lm1b.6

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We investigate the entanglement enhancement of the two-mode squeezed vacuum state using various combinations of photon additions and photon subtractions. We suppose that a sequence of N operations are performed on each mode and on a single mode of the two-mode squeezed vacuum state, each operation being photon addition or photon subtraction; then there are 2N possible combinations of operations in total. We calculate the entanglement for all the photon-added/subtracted states generated by all possible combinations for N=2, N=3, and N=4, respectively, and deduce that the combination of operations alternating between photon addition and photon subtraction enhances the entanglement most effectively, while adding or subtracting N photons repeatedly enhances the entanglement least effectively.
We investigate the problem of enhancing quantum entanglement of the two-mode squeezed vacuum state by asymmetric combinations of photon additions and subtractions. Suppose a combination of N operations is performed on the two-mode squeezed vacuum state, in which each operation may be either photon addition or photon subtraction and may be performed on either mode A or mode B of the state; then there are (N+1)2N possible combinations in all. We calculate in detail the entanglement enhancement by all possible combinations for each given N∈{1,2,…,5,6}, respectively, and find that when the squeezing parameter is small, combinations such as aa†aa†…, a†aa†a…, and their equivalent ones always achieve the greatest enhancement of entanglement, while combinations such as aaaa…, a†a†a†a†…, and their equivalent ones always achieve the lowest enhancement of entanglement; when the squeezing parameter is great enough, entanglement enhancement by each combination is nearly the same. We also compare the maximal and minimal entanglement achieved by such combinations for N=1 to 6, and find that when the squeezing parameter is small, a combination of more operations may generate even less entanglement than a combination of fewer operations.
The non-Gaussian operations effected by adding or subtracting a photon on entangled optical beams emerging from a parametric down-conversion process have been suggested to enhance entanglement. Heralded photon addition or subtraction is, as a matter of fact, at the heart of continuous-variable entanglement distillation. The use of such processes has recently been experimentally demonstrated in the context of the generation of optical coherent-state superpositions or the verification of canonical commutation relations. Here, we carry out a systematic study of the effect of local photon additions and subtractions on a two-mode squeezed vacuum state, showing that the entanglement generally increases with the number of such operations. This is analytically proven when additions or subtractions are restricted to one mode only, while we observe that the highest entanglement is achieved when these operations are equally shared between the two modes. We also note that adding photons typically provides a stronger entanglement enhancement than subtracting photons, while photon subtraction performs better in terms of energy efficiency. Furthermore, we analyze the interplay between entanglement and non-Gaussianity, showing that it is more subtle than previously expected.