Abstract

Schrödinger's dead-and-alive cat was a thought experiment applying the physics of electrons and atoms to our macroscopic world. New experiments with superconductors narrow the gap between theoretical ideas and reality.

Physics at the atomic scale is determined by the rules of quantum mechanics, which tell us that particles propagate like waves, and so can be described by a quantum-mechanical wavefunction. As an immediate consequence, a particle can be in two or more states at the same time — a so-called superposition of states. This curious behaviour has been hugely successful in describing physical systems at the microscopic level. For example, under the rules of quantum mechanics two atoms sharing an electron form a chemical bond, whereas in classical theory the electron remains confined to one atom and the bond can't form.

Applying quantum theory to our macroscopic world, Schrödinger¹ proposed a Gedanken or thought experiment with an unfortunate cat lingering in the twilight zone between life and death. This raised questions about whether quantum mechanics breaks down when the system is complex enough. On page 43 of this issue, Friedman et al.² go some way to answering this fundamental question by confirming that quantum superposition works as well in the macroscopic world of superconducting rings as it does in the microscopic world of photons, electrons and atoms.

Discussions about the boundary separating the microscopic quantum and macroscopic classical worlds sharpened up in the early 1980s, when Leggett and others suggested that a macroscopic system could behave quantum mechanically if it was suitably decoupled from its environment³. One of the systems under discussion was a superconducting quantum interference device (SQUID). This is a superconducting ring in which billions of paired-up electrons move in perfect harmony and without resistance. The question was whether a 'persistent' electric current in the ring would decay in a quantum-mechanical way (Fig. 1a). Subsequent experiments showed that currents in SQUIDs did indeed decay by a quantum-mechanical tunnelling process.

Figure 1: The state of Schrödinger's cat.

Physicists use potential wells to describe the preferred states of a system (the positions of electrons in a diatomic atom, the opposing currents in a superconducting ring, or the dead-and-alive state of Schrödinger's cat). A classical system trapped at the bottom of the well remains there because it needs a lot more energy to get out of the well. But a quantum particle trapped in a metastable state can tunnel out of the potential well (a). No energy is lost in the tunnelling process if the particle is isolated from its environment (blue), whereas coupling to the environment means the particle loses energy while tunnelling (weak coupling, magenta; strong coupling, red). b–d, A particle trapped in a double-well potential is localized in one of the wells if its coupling to the environment is large (b), if it hops incoherently back and forth between the wells at intermediate coupling (c), or if it coherently oscillates between the two wells with weak environmental coupling (d). The ground state of the quantum particle in d is lower because extending the wavefunction over both wells allows the particle to lower its energy; the first excited state comes to lie above zero energy. This is the origin of the coherence gap, 2, successfully measured by Friedman et al.¹ in their superconducting device. (E_B is the height of the energy barrier.)

High resolution image and legend (50K)

If a macroscopic system can decay by quantum tunnelling, the next question to ask is whether it could also oscillate back and forth between two states (Fig. 1b–d), say two states defined by currents flowing clockwise and anticlockwise in a SQUID. And if it can, would the macroscopic state tunnel back and forth sequentially, forgetting about its quantum-mechanical make-up after each hop, or would it oscillate coherently, preserving its quantum state throughout the hops? The second process goes under the name of 'macroscopic quantum coherence' and has been something of a holy grail in this field since the 1980s — it is the coherent superposition between the two current states in the ring that corresponds to the indeterminate state of Schrödinger's dead-and-alive cat.

Quantum theory predicts^{4, 5} that if such a system is strongly coupled to the environment, it remains localized in one state and so behaves classically (Fig. 1b). For intermediate coupling, the system hops randomly back and forth between the two states ( Fig. 1c). And finally, at low coupling, the system follows damped, coherent oscillations between the states, with the damping rate vanishing as the coupling to the environment goes to zero. This quantum mixing of the two states leads to a so-called coherence gap (2) separating the energies of the superposition states (Fig. 1d).

One explanation for this coherence gap is as follows. Consider a particle trapped in a potential well with two minima (a double-well potential). As the particle tunnels between the two wells, it lowers its kinetic energy because of the spreading of its wavefunction over both wells. As a result, the new mixed ground state is shifted down by with respect to the energy of the individual wells. This 'symmetrical' state always comes with an 'antisymmetric' partner state, which is slightly higher in energy. In fact, this excited state comes to lie at an energy above the original well energy, resulting in an excitation gap of 2. This phenomenon is well known in chemistry, where the two mixed or superposition states correspond to the bonding and antibonding states of a diatomic molecule.

Measuring this coherence gap in a macroscopic device, such as a SQUID, is a tricky business because the quantum superposition is extremely sensitive to external noise. Experimentalists have been trying to do this for years with no conclusive results. In their experiment, Friedman et al.² use a SQUID with two current states flowing clockwise and anticlockwise. Starting with a specific current state, say clockwise, they then bathe the SQUID in microwaves and measure the probability of finding the current flowing in the opposite — that is, anticlockwise — direction. This probability peaks when the microwave frequency matches up with the two superposition states, allowing them to identify a coherence gap of 0.01 millielectron volts (corresponding to a temperature measurement of 0.1 Kelvin). The size of the gap puts an upper limit on the decoherence rate of the device — that is, the rate at which it decays into a classical state — and allows them to assess the quality of their experimental set-up.

How does this experiment achieve what was previously impossible? Rather than using the ground states of their potential wells, Friedman et al. use high-energy microwaves to shift their coherence experiment up to energy states close to the top of the potential barrier, thereby increasing the tunnelling rate between the two wells by many orders of magnitude. The challenge in future experiments will be to track the appearance of this coherence gap when probing lower-energy (semiclassical) states deeper in the well. Another possibility would be to make the coherence gap vanish by introducing artificial decoherence into the system, for example by coupling the SQUID to a metallic reservoir.

So quantum theory does not break down when the system becomes more complex — here, there are billions of electron pairs acting in unison. Are there reasons to suspect that it will break down elsewhere? Most physicists would bet that quantum theory is safe, and that, where it does 'break down', this is because of coupling to the environment inducing decoherence. Besides these philosophical implications, the experiment of Friedman et al. has practical relevance, particularly in the newly emerging field of quantum computing. For physical systems to operate as quantum bits and logic gates they have to deal with two conflicting requirements: on one hand, the quantum bits have to be manipulated in order to carry out the operations required by the computing algorithm; on the other hand, the whole quantum computer must be decoupled from the environment as much as possible in order to preserve its quantum coherence.

Proposals for quantum bits put forward by the quantum optics community are usually based on individual photons or atoms, and have the advantage of being decoupled from the environment. More recently, solid-state systems based on nano-engineered superconducting devices have been proposed as quantum bits, with the advantage that they are easy to manipulate. The first 'superconducting-charge qubit' was built last year by Nakamura et al.⁶. They reported real-time observations of coherent charge oscillations on a small superconducting island. But as with coherence experiments on single photons or atoms, this experiment deals with the coherent propagation of individual electron pairs. What is truly amazing about the new experiment of Friedman et al.² is that the tunnelling object is a magnetic flux set up by billions of electron pairs coherently circulating within a superconducting ring. With the discovery of coherence in such a macroscopic system, Schrödinger's cat has put on quite a bit of weight.

References

1. Schrödinger, E. Naturwissenschaften 23, 807–812, 823–828, 844–849 ( 1935). | ISI |
2. Friedman, J. R. , Patel, V. , Chen, W. , Tolpygo, S. K. & Lukens, J. E. Nature 406, 43– 46 (2000). | Article | PubMed | ISI | ChemPort |
3. Caldeira, A. O. & Leggett, A. J. Ann. Phys. 149, 374–456 ( 1983). | ISI |
4. Schmid, A. Phys. Rev. Lett. 51, 1506–1509 (1983). | Article | ISI |
5. Chakravarty, S. & Leggett, A. J. Phys. Rev. Lett. 52, 5–8 ( 1984).
6. Nakamura, Y. , Pashkin, Yu. A. & Tsai, J. S. Nature 398, 786– 788 (1999). | Article | ISI | ChemPort |