Realistic conversion of single-mode squeezed vacuum state to large-amplitude high-fidelity Schrödinger cat states by inefficient photon number resolving detection

Abstract

Abstract We theoretically propose an efficient way to generate optical analogs of both even and odd Schrӧdinger cat states (SCSs) of large amplitude with high fidelity and reasonable generation rate. The resources consumed are a single-mode squeezed vacuum state (SMSV) and possibly a single photon or nothing. We report the generation of even (odd) SCS with amplitude <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>4.2</mml:mn> <mml:mo>,</mml:mo> </mml:math> fidelity higher than <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>0.99</mml:mn> </mml:math> with success probability a little more than <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>7</mml:mn> </mml:mrow> </mml:msup> </mml:math> by subtraction of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>30</mml:mn> <mml:mo stretchy="false">(</mml:mo> <mml:mn>31</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:math> photons from SMSV by ideal photon number detection. In order to reduce the requirements for the sensitivity of photon number resolving (PNR) detector, we show the implementation of even/odd SCSs with the same characteristics with two PNR detectors resolving only <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>15</mml:mn> </mml:math> photons each instead of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>30</mml:mn> <mml:mo>.</mml:mo> </mml:math> In the case of inefficient detector, SCS’s size and its fidelity can be kept close to perfect by using highly transmitting beam splitter, but at the cost of very dramatic reduction of the success probability. In order to have certain harmony between the characteristics (large amplitude, high fidelity and acceptable success probability) in the case of imperfect detection, highly transmitting beam splitters should not be used and number of the subtracted photons must be reduced to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>10</mml:mn> <mml:mrow> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mn>11</mml:mn> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mo>.</mml:mo> </mml:math>

Topics & Concepts