Using one’s resources in the most efficient way possible is desirable for several reasons: we save time, we save efforts, we save money. The same holds true, of course, in our labs. There is even a rich literature on “resource theories”, which study what can be done with limited means. In a very similar vein, Sparaciari and coworkers asked themselves how well one can detect phase variations between two modes without using particularly fancy equipment. Of course, one could in principle concoct an even more sensitive setup that requires extravagant quantum states, but the gains are probably not going to justify the effort. So their question is very relevant and also very timely when we recall that such precise measurements are at the core of important experiments, e.g. the detection of elusive gravitational waves.
Measurements of phase variations have already reached the standard quantum limit (SQL), but there are some tricks we can play to go even further, for instance by employing squeezed light. The idea behind squeezed light is simple: we know we cannot beat Heisenberg’s uncertainty relation Dx Dp > h, but nobody prevents us from decreasing, say, the uncertainty Dx at the expense of increasing the uncertainty Dp, as long as their product is still larger than h. So squeezed light provides a highly sensitive reference for further measurements of one particular quantity.
The question is now, how far can we take it? Sparaciari and coworkers calculated the largest possible phase sensitivity that we can achieve in an interferometer in two scenarios: in the first we are allowed to use squeezed light and a passive optical medium and in the second we can use only coherent light (unsqueezed) and an active optical medium (which does some squeezing for us).
Their findings tell us that not only do these setups already allow us to achieve Heisenberg scaling, but (perhaps surprisingly to some of us) we can do better with passive optical devices and squeezed light than with active optical devices and coherent light. In particular, the best sensitivity is achieved with a pair of identical squeezed states, with at most one third of the total energy dedicated to squeezing. This means that if we keep things simple (i.e. we don’t waste a lot of energy, time and money on fancy quantum sources such as NOON states) we can still achieve an optimal sensitivity with a passive interferometer and furthermore we can actually do better than with an active one. So yeah, sometimes less is more.
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