October 2015
Spotlight Summary by Filippo Miatto
Two-mode squeezed states as Schrödinger cat-like states
When Erwin Schrödinger concocted his gedankenexperiment, he managed to phrase a very deep problem in quantum mechanics in terms that everyone could understand. However, the metaphor that he used is too extreme to be taken seriously, as cats are classical objects after all. In fact, what scientists refer to as actual "cat states" are a superposition of two classically-looking quantum states. The only way they can resemble classical states is by being "large" in some sense, which is why cat states are also referred to as "macroscopic superpositions". However, this makes such superpositions very tricky to generate.
The typical cat state in the literature is a superposition of two coherent states (the states of a laser beam) with opposite phase. This seems like a good choice, because coherent states are the most 'classical' of all the states of the radiation field and the more intense they are the more classically they behave, but producing a coherent superposition of large coherent states is very challenging.
Oudot and colleagues, from the University of Basel, propose a different type of cat state whose generation is not problematic at all. The idea is to use the so called "two-mode squeezed vacuum" states, which can be generated by pumping a nonlinear crystal with a strong enough laser beam. What they realized is that one only has to adjust which property is the one to be regarded as "large". To demonstrate their intuition they used an operational criterion to regard a state as macroscopic, which is by doing state discrimination with only coarse-grained measurements (i.e. measurements that do not possess high resolution). In this framework one can distinguish macroscopic and microscopic states as those that can and cannot be differentiated by a coarse-grained measurement, despite all such states being orthogonal in a quantum-mechanical sense. They found that with a coarse-grain measurement that only measures the sign of a quadrature (say, the X quadrature) it is more and more likely to identify the two states correctly as the squeezing parameter increases. Their conclusion is that the quadratures in the two phase spaces (recall that these are two-mode states) become macroscopically correlated as the squeezing increases.
This realization could have a profound impact on the way we think of macroscopic superpositions. In the history of science, it happens occasionally that while the community is fixated on a specific way of doing something, somebody comes along with a much simpler solution. I believe this might be one of those events.
You must log in to add comments.
The typical cat state in the literature is a superposition of two coherent states (the states of a laser beam) with opposite phase. This seems like a good choice, because coherent states are the most 'classical' of all the states of the radiation field and the more intense they are the more classically they behave, but producing a coherent superposition of large coherent states is very challenging.
Oudot and colleagues, from the University of Basel, propose a different type of cat state whose generation is not problematic at all. The idea is to use the so called "two-mode squeezed vacuum" states, which can be generated by pumping a nonlinear crystal with a strong enough laser beam. What they realized is that one only has to adjust which property is the one to be regarded as "large". To demonstrate their intuition they used an operational criterion to regard a state as macroscopic, which is by doing state discrimination with only coarse-grained measurements (i.e. measurements that do not possess high resolution). In this framework one can distinguish macroscopic and microscopic states as those that can and cannot be differentiated by a coarse-grained measurement, despite all such states being orthogonal in a quantum-mechanical sense. They found that with a coarse-grain measurement that only measures the sign of a quadrature (say, the X quadrature) it is more and more likely to identify the two states correctly as the squeezing parameter increases. Their conclusion is that the quadratures in the two phase spaces (recall that these are two-mode states) become macroscopically correlated as the squeezing increases.
This realization could have a profound impact on the way we think of macroscopic superpositions. In the history of science, it happens occasionally that while the community is fixated on a specific way of doing something, somebody comes along with a much simpler solution. I believe this might be one of those events.
Add Comment
You must log in to add comments.
Article Information
Two-mode squeezed states as Schrödinger cat-like states
E. Oudot, P. Sekatski, F. Fröwis, N. Gisin, and N. Sangouard
J. Opt. Soc. Am. B 32(10) 2190-2197 (2015) View: Abstract | HTML | PDF