A tiny shift in quantum energy levels usually associated with individual atoms has been seen in a solid for the first time by physicists in Switzerland and Canada. The team spotted the Lamb shift in a small piece of superconductor that functions as a quantum bit or “qubit”.

The interactions that cause the Lamb shift are also responsible for making qubits unstable, and therefore the team believes that insights from their experiments could be used to create more robust qubits that could be used in quantum computers.

The Lamb shift is a tiny change in certain atomic energy levels. It occurs because the atom is interacting with the empty space surrounding it by absorbing and emitting “virtual” photons. Discovered in 1947 by the American physicist Willis Lamb, the shift provided important experimental evidence for the then emerging theory of quantum electrodynamics (QED), which describes the interaction of charged particles in terms of the exchange of photons.

While the Lamb shift should also affect electrons in a solid, it has proven difficult to see because electron energy levels in solids are wide bands, rather than discrete atomic levels.

Shifting transmon

Now, Andreas Wallraff and colleagues at ETH Zurich in Switzerland and the University of Sherbrooke in Quebec have spotted the Lamb shift in the energy levels of a qubit called a “transmon”, which is made from two tiny pieces of superconductor connected by two tunnel junctions (Science 322 1357).

The superconductor contains a large number of “Cooper pairs” of electrons that can move through the material without any electrical resistance. The energy levels of the qubit are defined by the precise distribution of Cooper pairs between the two tiny pieces of superconductor.

The team’s transmon is placed in a microwave cavity and its shape was chosen to give it a large electrical dipole moment. This increases the strength at which it interacts with both microwave photons and the virtual photons of the vacuum. In addition, the shape and size of the cavity were designed to enhance the photon’s electric field in the region of the qubit.

Transitions between qubit energy levels occur when electrons in the superconductor collectively absorb or emit photons at certain wavelengths. This process can be enhanced by tuning the frequency of microwave radiation injected into the cavity so that a single photon of the correct wavelength bounces back and forth across the qubit many times.

In their experiment, the team used a cavity to enhance the effect of the virtual photons related to the Lamb shift — which makes it more likely that the qubit absorbs and emits virtual photons. Indeed, Wallraff and colleagues measured a cavity-enhanced shift of 1% in the difference between the two energy levels. This is 10,000 times greater than the Lamb shift seen in hydrogen without a cavity.

Tricky measurement

Despite its relative magnitude Wallraff told physicsworld.com that the tricky part of the experiment was measuring the shift. This is because any measurement on the qubit must be made using photons as a probe — and their presence in the waveguide could cause a shift in the energy levels (the a.c. Stark effect), which would overwhelm the Lamb shift.

To get around this problem, the team used a very small number of probe photons that were off-resonance with the cavity. This means that they remain in the region of the qubit only long enough to measure the transition energy but not cause any a.c. Stark shifts.

The discovery of such a large Lamb shift is a mixed blessing for those trying to design practical qubits. On one hand, the virtual photons induce spontaneous emission in qubits, which limits their usefulness for quantum computing. On the other hand, Wallraff and colleagues have established that the Lamb shift can be minimized in a transmon qubit if it is set far from resonance with the virtual photons. This suggests a way of making qubits more robust, as demonstrated in a recent work by a Robert Schoelkopf and colleagues at at Yale University (Phys. Rev. Lett. 101 080502).

Detecting the Lamb shift in a solid system also suggests the possibility of seeing the effects of other virtual particles such as phonons — which are quantized vibrations in solids. According to Wallraff, such an acoustical Lamb shift due to the mechanical quantum fluctuations of nanometer-scale electromechanical oscillators could similarly affect the energy levels of a qubit.