Harvesting asymmetric steering via non-identical detectors

Abstract We investigate asymmetric steering harvesting phenomenon involving two non-identical inertial detectors with different energy gaps, which interact locally with vacuum massless scalar fields. Our study assumes that the energy gap of detector B exceeds that of detector A . It is shown that $$A\rightarrow B$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>→</mml:mo> <mml:mi>B</mml:mi> </mml:mrow> </mml:math> steerability is bigger that $$B\rightarrow A$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>B</mml:mi> <mml:mo>→</mml:mo> <mml:mi>A</mml:mi> </mml:mrow> </mml:math> steerability, implying that the observer with a small energy gap has more stronger steerability than the other one. We find that the energy gap difference can enlarge the harvesting-achievable range of $$A\rightarrow B$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>→</mml:mo> <mml:mi>B</mml:mi> </mml:mrow> </mml:math> steering, while it can also narrow the harvesting-achievable range of $$B\rightarrow A$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>B</mml:mi> <mml:mo>→</mml:mo> <mml:mi>A</mml:mi> </mml:mrow> </mml:math> steering at the same time. In addition, the maximal steering asymmetry indicates the transformation between two-way steering and one-way steering in some cases, showing that $$B\rightarrow A$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>B</mml:mi> <mml:mo>→</mml:mo> <mml:mi>A</mml:mi> </mml:mrow> </mml:math> steering suffers “sudden death” at the point of this parameter. These results suggest that asymmetric steering exhibits richer and more interesting properties than quantum entanglement harvested from vacuum quantum field.