...Imagine it is deep winter in Finland, where I am based at Aalto University, and the temperature outside is -30 degrees Celsius. A nicely warmed sauna at 80 degrees Celsius would surely be welcome for warming up. Getting in the sauna, then directly out in the freezing cold is an "extreme" experience that many people actually enjoy a lot. If you are one of those, and assuming that you spend roughly the same amount of time outside in the cold and in the sauna, the average temperature you see is a perfect 25 degrees Celsius. Welcome to sunny California! Well, not really...
Yet, as it turns out, switching between states with different chemical potential is something that particles in various many-body ensembles experience, and indeed this phenomenon has been seen before in NMR (nuclear magnetic resonance). An experiment recently carried out by our group at Aalto (with theory support from Oulu University) looking into this effect shows that it could have relevance for quantum computation. Quantum computers process information encoded onto "qubits" (or "quantum bits"). For example, the polarization state of photons is typically used in quantum-optics experiments. In our case, we employ the oscillatory states of an electrical circuit, realized with Josephson junctions and superconductors. The quantum bits can not only exist in one or the other of two states (like binary digits 0 and 1), but also as a superposition of both states simultaneously--allowing, in theory, for much more powerful processing.
In our experiment we simulate the effect of switching the chemical potential using a circuit comprising a qubit and a measuring cavity by changing the qubit frequency between two distinct values (J.Li et. al., Nat. Commun. 4, 1420 (2013)). We keep track of this frequency by monitoring the interaction between microwave radiation and the qubit, which results in distinctive lines in the absorption spectrum at certain frequencies.
Motional averaging under a random modulation
Now, you might expect that we would see two spectral lines, one corresponding to each of the frequency extremes--in much the same way as our Finnish sauna fan would register two very different temperatures if he or she jumped from the sauna to the snow. That is indeed what we saw when the switching was done slowly. But surprisingly, when the change was faster than a critical value (the inverse of the qubit frequency separation) the two lines merge into a single one. The image on the right shows motional averaging under a random modulation (pulse pattern in white). The figure presents the spectrum (horizontal axis is frequency) at increasing jump frequencies (vertical axis).
The effect can be interpreted as meaning that our ability of distinguishing between the two values of the qubit frequency is impaired by the fast switching. Indeed, the single (motional-averaged) spectral line is formed precisely when the jumping rate exceeds the bound set by the time-energy uncertainty relation,
[equation]{\Delta} t {\sim} {\frac{\hbar}{\Delta E}}[/equation]
Why is this important? One of the biggest hurdles to building a quantum computer is that the quantum effects on which it relies are fragile and can easily be destroyed by decoherence, as the qubits cannot be totally isolated. The motional averaging experiment suggest a new route to improving the decoherence times of the existing qubits. If the noise entering from the environment in such a device fluctuates slowly, it will have a disruptive effect, for example displacing the frequency of the qubit between two extremes. But if this noise can be made faster than a threshold value, the qubit will effectively be at one stable frequency, reducing the so-called dephasing rate. Paradoxically, one can fight noise with even more noise! Indeed, the group has demonstrated that the motional-averaged line preserves the quantum coherence of the original qubit and elementary quantum operations can be performed.
So how fast one has to jump in and out of the sauna to experience a perfect 25 Celsius? According to the calculations in our paper, you have to jump, on average, more than roughly 10 thousand billion times per second!
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Gheorghe Sorin Paraoanu is a physicist at Aalto University and a member of FQXi.