Steele Lab

Quantum Circuits and Mechanics

In optomechanics, light is used to control and detect mechanical motion. In order to achieve quantum superposition states of motion, researchers are in search of a platform which promises strong coupling between light and motion at single-photon level.

Recently, Yuan et al. from the SteeleLab have introduced a new optomechanical platform based on 3D superconducting cavities in Nature Communications. For the first time, researchers couple the mechanical motion of a silicon nitride membrane to electromagnetic field inside the 3D microwave cavity. Exploiting the large quality factors of both the cavity and the membrane, they are able to use microwave photons to cool the motion of the millimetre scale membrane resonator, visible to the naked eye, to a record low mode temperature of 34 microkelvin.

The result demonstrates the potentials of 3D optomechanics. With optimization, this platform offers the possibility to reach the regime of single-photon strong coupling, opening up a new generation of experiments.

For more information, see the article on the Nature Communications website, as well as the press release from TU Delft.

 

Coherence is a widely used concept in quantum mechanics. When a quantum system interacts with its environment, the loss of information about the phase of quantum states is defined as decoherence. Decoherence plays a crucial role in quantum information processing: in contrast to classical bits that suffer only from relaxation in the form of bit flips (loss of energy), quantum bits are much more fragile as their state can also be lost by decoherence of the phase information stored in quantum superpositions. As mechanical objects are now reaching the quantum regime, it is interesting to think about how the concept of decoherence can be applied to the motion of a mechanical resonator.

In their work in Nature Communications, Schneider et al. have explored the concept of decoherence applied to a mechanical resonator. By studying very sensitive nanotube mechanical resonators at low temperatures using a new, high-speed detection technique, they were able to observe and identify a process of decoherence in the motion of a carbon nanotube.

Figure: Electron microscope image of a suspended carbon nanotube (white curling string) suspended between two metal electrodes (blue). The carbon nanotube is only 1 nm (about 10 atoms) in diameter. Near the trench, the nanotube sticks to the metal and is pulled into a tight string that can vibrate like a guitar string. The blue electrodes are also used for injecting and detecting current flowing through the nanotube, which is used to sense the nanotube motion. Below the nanotube is a local gate (yellow) that is used to shake the nanotube string, making it vibrate..

What does “decoherence” mean for a mechanical resonator? Similar to the loss of information of the phase of a quantum superposition of a qubit, decoherence in a mechanical resonator corresponds to the loss of information about the phase of the oscillations in the position of the mechanical object. In the animation shown below, we show side-by-side the processes of oscillation, relaxation, and decoherence for a quantum bit and a mechanical resonator. In both cases, the loss of phase information comes in through random fluctuations of the frequency of the motion, where “motion” for the qubit corresponds to oscillations of the Bloch vector, while for the mechanical resonator, “motion” is simply the oscillations of it’s position.

Movie sequence: A sequence of videos showing (i) how to relate the evolution of a quantum superposition of a qubit to the motion of a mechanical resonator (ii) how to visualize the decay of a qubit and the damping of motion, (iii) the effect of dephasing on the coherence of a qubit and on the motion of a vibrating string, and (iv) the combined effects of dissipation and dephasing on qubits and mechanical motion. See the description box on the youtube pages for a detailed explanation of the videos.

To visualize this, it is useful to think about the motion of a guitar string. When you pluck a guitar string, it will vibrate up and down at its resonance frequency, and after some time, this motion will slowly decay as they lose energy. The vibrations in the string lose energy due to damping from the air and transmitting sounds into the guitar body and the room. This process of losing energy is called dissipation.

Another related effect, which is often overlooked in the response of mechanical resonators, is dephasing. Dephasing, which leads to decoherence, and in this case, rather than losing energy, instead the frequency of the oscillation is changing randomly in time: imagine, for example, that someone was turning the tuning screw on the guitar string while it was vibrating without you knowing about it. These random fluctuations in the frequency will make you lose track of the phase of the oscillations of the string since sometimes it will vibrate a bit faster, and sometimes a bit slower. You can “hear” the type of sound that such a “bad” qubit would make in this youtube video here:

In the experiment, by measuring the mechanical response of the nanotube in two different ways, one “spectral” technique by slowly sweeping the frequency, and one “ring down” technique by plucking the nanotube and looking at how low it takes for the sound to decay, Schneider et al observed that the nanotube in their experiment was not only subject to dissipation (energy loss), as assumed in all previous nanotube experiments, but it is also influenced by dephasing that caused decoherence of its motion.

Although the experiments were performed in the classical regime, the concepts identified in the classical motion would also apply directly to quantum superpositions of mechanical motion, a goal of the current research in quantum mechanical resonators.

For more information, see the article here in Nature Communications and also the press release on the TU Delft website.

In physics, we are used to thinking about the motion of electrons driven by electric fields: electrons are attracted to regions of lower electrostatic potential, like a ball rolling down a hill. When we put a voltage across a resistor, electrons feel a force from the electric field and flow like a river to the place of lowest potential. The effect of electrons flowing “downhill” is also the basis of solar cells, in which they flow in response to the built-in electrostatic voltage in a semiconductor PN junction and generate a current when it is exposed to light.

In their work reported in Nature Communications, Gilles Buchs and Salvatore Bagiante, working with Gary Steele in the SteeleLab, have demonstrated that this is not always the case, and in particular, electrons can sometimes be induced to flow “uphill”.

Left: Schematic of the photocurrent imaging experiment with a double-gated suspended carbon nantoube. Right: Observed photocurrent for different doping configurations induced by the gates. In the upper right “pp” region, the sign of the photocurrent indicates that electrons are flowing “uphill” in response to the light

Their work is based on a double-gated semiconducting carbon nanotube, in which the doping level in different parts of the device can be controlled using local gates. Measuring the photo-induced current across the device as the doping levels were changed, Buchs et al. showed that at certain gate voltages, the sign of the current indicated that electrons were flowing “uphill”, against an electric field. This results from the photothemoelectric effect, in which the flow of electrons is driven by differences in chemical potential rather than electrostatic voltage.

The new work solves contradicting reports in the nanotube community about photocurrent generation mechanisms in semiconducting carbon nanotubes, and lays an important framework for interpreting signals in scannning photocurrent microscopy, a technique widely applied to other materials such as graphene, 2D semiconductors, and semiconducting nanowires.

For more information, see the article in Nature Communications, also covered in an article on nanowerk.com. The authors would also like to thank Val Zwiller for experimental support during the project.

Graphene is famous for the relativistic way that electrons in the material move, but more recently, researchers have started studying how the graphene sheet itself moves when you make it into a mechanical resonator like a drumhead.

In our work in Nature Nanotechnology, we have used a superconducting microwave cavity coupled to a graphene membrane to study the drum’s motion at milliKelvin temperatures. By peeling off a graphene flake on top of a superconducting metal used to trap microwave photons, Singh et al from the SteeleLab have used microwave “light” to detect the position of the membrane. By bouncing this light off of the graphene sheet, which acts as a moving “mirror”, the researchers were also able to “beat the drum”, shaking it using the radiation pressure from the momentum of light.

For more information, including an animation of the microwave photons bouncing off the drum, see our press release on the TU-Delft website.

Left: Colorized electron microscope image of the graphene drum used in the experiment. The blue shows the graphene sheet, the yellow shows the superconducting metal that forms the cavity. Right: An artist impression of microwave photons (yellow comets and glow) propagating in the gaps of the superconducting waveguide and interacting with the graphene drum (transparent sheet).

While the spin-orbit coupling in carbon nanotubes was originally thought to be small due to the light atomic mass of the carbon nucleus, it turns out that the p-like nature of the electron orbitals combined with the curvature of the nanotube surface can lead to a measurable spin-orbit gap in carbon nanotube quantum dots.

In their work published in Nature Communications, Steele et al found that the spin orbit coupling was even larger than expected, raising new questions about the nature of electronic states in few-electron carbon nanotube quantum dots.