Goals

The ULT team performs condensed matter experiments down to the microkelvin temperature range. We study model systems and develop the state-of-art techniques required by these demanding experiments, building on the capabilities of the Néel laboratory. The physics involved concerns quantum fluids, amorphous matter and fundamental aspects of microwave opto-nano-mechanics. The group is part of the European Microkelvin Platform, a “laboratory without walls” federating ultra-low temperature physics at the European level.

WebMaster: E.C. 2020

Micro/Nano-mechanics

Currently there is great enthusiasm for the experimental realization and study of MEMS (micro-electro-mechanical-systems) and the even smaller NEMS (nano-electro-mechanical-systems). MEMS are usually made of silicon, but sometimes other materials such as GaAs or diamond are used. They have many technological applications, ranging from accelerometers in airbags and microphones in iPhones to more surprising objects such as electro-mechanical chips dedicated to biology. On the other hand, NEMS are mainly a subject of fundamental research at present because of fabrication and measurement difficulties.

The mechanics of these micro and nanoscale objects is obviously interesting: we can study relaxation  and non-linear phenomena for example. But why study these systems at ultra-low temperatures? For three reasons, which correspond to our research projects:

Ideal Conditions

At low temperatures the physical conditions are well controlled and conducive to high quality measurements: the electrical noise is lower than at ambient temperature, the vacuum in the experimental chamber is excellent, the attainable magnetic fields are higher, and superconducting materials can be used. Finally, the physical properties of the materials themselves are often better (less mechanical dissipation, greater stiffness) and easier to interpret (only low energy states are populated). Thus, whatever the micro or nano-mechanical properties studied, the physical conditions are ideal.

Probes

Micro and nanomechanical systems can serve as probes for low temperature physics. They can be used to study superconductivity, for example, by measuring the magnetic force experienced by a superconducting structure when it is subjected to a magnetic field. For our studies, what interests us is to use MEMS and NEMS to probe quantum fluids and the mechanical properties of the solid materials that constitute them. For example, the mechanical dissipation of energy at low temperatures is governed by the quantum tunneling of two-level systems present in structures. This physics, linked to the physics of glasses, is only partially understood in NEMS.

In the study of quantum fluids, mechanical oscillators are often used as viscometers. If the temperature dependence of the viscosity of the fluid is known, the mechanical oscillator can then be used as a thermometer. This viscosimetry of quantum fluids has also recently developed towards quantum turbulence [1]. The mechanical resonator can both generate this turbulence and detect it. Finally, with NEMS it is now possible to probe the superfluid 3He at a length scale of the order of its coherence length x0, which is essentially the size of the Cooper pair which represents the very particular quantum state fluid. We are interested in the low temperature mechanical characterization of these oscillators (typically from 100 µK to 30 K). Preliminary tests in 4He were carried out [2], as well as in superfluid 3He-B in collaboration with Lancaster University.

As an alternative to conventional approaches, the Helsinki team also proposed using quartz tuning forks (the same as those used for the time base of watches) for the study of quantum fluids. Many teams have adopted them because of their ease of use.

Beyond the study of (quantum) fluids at low temperature, viscosimetry, and precision thermometry, the realization of silicon oscillators with rather special geometries has as a direct (« technological ») application in the ULTIMA project (detection of dark matter), by optimizing superfluid 3He bolometers.

As an example, here is a micrograph of a vibrating silicon wire [3].

Microfabricated silicon vibrating wire for thermometry in 3He-B. Its mechanical characteristics are excellent.

Such oscillators could replace conventional vibrating wires to produce high performance thermometers around 100 µK.
These oscillators are made from a silicon wafer, in which a window has been chemically etched, leaving only a thin membrane on one side (typically 10 µm thick). This membrane is covered with metal, and structured by reactive ion etching (RIE). The oscillating structure is the silicon « goal post », covered with a layer of metal (here niobium, a low-temperature superconductor).

Model Sytems

MEMS and NEMS studied at the lowest temperatures are above all model systems for those interested in mechanics per se [4]. Non-linear dynamics, an extremely rich field, can be studied there under optimal conditions. In the case of NEMS, the resonance frequencies are very high (from 1 to 100 MHz typically). Different geometries and materials are used, e.g., silicon goal-posts and doubly clamped silicon nitride beams (see images below ). The latter material has demonstrated exceptional mechanical properties, and is now widely used by the NEMS community.

If the temperature T is high with respect to the resonance frequency characteristic of a mechanical mode ω_n, then many phonons populate the mode in question and its dynamics will be described by classical mechanics. Conversely, when k_BT << ħω_n, the mechanical mode reaches the quantum limit. The different fundamental aspects of these two regimes are discussed below.

Here is a nanomechanical silicon wire.

NEMS of the same geometry as the micro-oscillators already studied. The width and thickness of the structure is 200 nm and the length is approximately 10 μm.

These oscillators are made from an SOI (silicon on insulator) wafer whose sacrificial oxide layer is etched by hydrofluoric acid (HF). A full layer of aluminum is deposited to contact the system. The sample was fabricated in collaboration with Olivier Bourgeois of the Institut Néel. At the top the gate electrode is separated from the oscillator by a gap that can be reduced to less than 100 nm.

Here is a doubly clamped beam NEMS.

Highly strained silicon nitride NEMS in the form of a doubly clamped beam. The width and thickness of the structure is 200 nm and the length is about 15 µm.

These oscillators are made from a silicon wafer covered with highly strained silicon nitride. The silicon is etched with very high selectivity by XeF2 gas. An aluminum metal layer is deposited to form the electrical contacts.

Model systems: micro and nano-mechanical at low temperature
When (at least) one dimension of the system is submicron, we reach the realm of nanomechanics. Several questions are posed by these new objects, for example: do theories that are valid on large length scales successfully explain the mechanical behavior of these tiny devices? Can we again explain the non-linear regimes of these nanobeams in simple manner? What will happen when these mechanical oscillators are cold enough to theoretically be in their quantum ground state?

Our team is developing this path, in collaboration with Olivier Bourgeois from the Institut Néel (thermodynamics group for small systems). The structures can be actuated by the Lorentz force (as for a vibrating wire), or by using an electrical force generated by a voltage applied to the gate electrode close to the structure (see SEM images above ). In these studies, temperature becomes a control parameter that tells us about the underlying physical mechanisms.

[1] D.I. Bradley, D.O. Clubb, S.N. Fisher, A.M. Guénault, R.P. Haley, C.J. Matthews, G.R. Pickett, V. Tsepelin, and K. Zaki, Emission of Discrete Vortex Rings by a Vibrating Grid In Superfluid 3He-B : A Precursor to Quantum Turbulence, Phys. Rev. Lett., 95, 035302 (2005); R. Hänninen, M. Tsubota, W. F. Vinen, Generation of turbulence by oscillating structures in superfluid helium at very low temperatures, Phys. Rev. B 75, 064502 (2007).

[2] Eddy Collin, Laure Filleau, Thierry Fournier, Yuriy M. Bunkov and Henri Godfrin, Silicon Vibrating Wires at Low Temperatures, J. of Low Temp. Phys., 150, 739 (2008).

[3] S. Triqueneaux, E. Collin, D.J. Cousins, T. Fournier, C. Bäuerle, Yu.M. Bunkov, H. Godfrin, Microfabrication of silicon vibrating wires, Physica B, 284, 2141 (2000)

[4] A.N. Cleland, Foundations of nanomechanics, Springer (2003)

Amorphous Matter

Schematic of a nanobeam containing two-level systems (TLS), whose dynamics are described by a double-well potential.

One of the themes pursued by the group is the study of amorphous materials at the lowest temperatures. These materials, which are found in everyday life due to many of their unique properties, are still poorly understood on a microscopic scale. Paradoxically, although glasses are like liquids in that they do not have long range order, they are rigid.

The low temperature properties of glasses are particularly intriguing. Below 1 Kelvin, the thermal and mechanical behavior of glasses is very different from that of crystals, and it implies the existence of a certain type of low energy excitation (LEE) which is not present in crystals. It is known that these LEEs are generally not impurities, but are intrinsic to glass because the same low temperature characteristics are also observed for ultra-pure specimens.

The true identity of these LEEs is a long-standing question still open today. The most discussed candidates are two-level systems (TLS), which can « tunnel » between two quasi-equivalent energy states (see figure above). But they have only been identified in certain materials so far. In addition, the mechanical dissipation in amorphous solids is remarkably universal around the 1 kelvin, varying only by about an order of magnitude in the quality factor Q^-1 ~ 3 × 10^-4 despite enormous variation in composition, impurity concentration and structure. 

Solving these puzzles has been a daunting task that has occupied physicists for decades. We address these problems using a range of low temperature techniques, from proven techniques (such as the « Double-Paddle Oscillator », a micro-mechanical structure on which an amorphous film is deposited) to radically new approaches.

Low temperatures are achieved using dilution cryostats in combination with nuclear adiabatic demagnetization. An ultimate goal is to individually control the TLS present in the material, in a coherent way (in the quantum sense). To do this, the amorphous material must constitute a nano-mechanical resonator operated in its fundamental quantum state, below 1 mK (see figure above).

Quantum Fluids & Solids

QFS. Neutron scattering, NMR. Vibrating wires.

Cryogenics

The Ultra-low temperature team is depositary of the sub-milliKelvin nuclear demagnetisation technology at CNRS. Besides, the team possesses two commercial (« dry ») dilution cryostats that reach base temperature of 8 mK. These machines are autonomous and do not require liquid helium to cool down: they have a pre-cooling stage based on a pulse-tube cooler reaching about 3 K. They work on the same principle as « wet » machines to reach the sub-Kelvin range: the dilution of ³He into ⁴He. A schematic of the principle is given below:

This represents the so-called « mixing chamber » of the cryostat. This is the place where the mixture separates in a pure phase of ³He (dark green) floating on top of a heavier phase of ⁴He containing about 6% of dissolved ³He (light green). By means of a pumping system (at room temperature), a flow of ³He is forced through the machine (yellow arrows). When these atoms cross the boundary and dilute into ⁴He, they absorb heat: the cooling power of this mechanism goes at low temperatures as dn/dt T² with dn/dt the flow of ³He atoms and T the mixture temperature. Our machines typically have 20 µW of cooling power at 20 mK. More information can be found in e.g. F. Pobell, Matter and Methods at Low Temperatures, Springer (2007).

Our team has also a home-made nuclear adiabatic demagnetization cryostat that reaches temperatures of the order of 100 µK, and is developing a second such equipment. The machine is built around a first stage that is a conventional dilution unit, connected through a « heat switch » to the « copper nuclear stage ». A picture of the cryostat is shown below, with its plastic mixing chamber and the copper stage underneath it. The microwave wiring of our experiments is also visible.

The heat switch is made of a piece of aluminium inserted in a small coil. When there is no current in the coil, the aluminium is free of magnetic field and superconducting: it does not conduct heat (the switch is « open »). When we pass a small current in the coil, a small field applied on the aluminium makes it normal: it is then a very good metal conducting heat (it is « closed »).

The technique is single-shot: one first pre-cools the copper stage in a high magnetic field B_ini (about 7 T), with the heat switch « closed ». This takes about a week to reach T_ini  ≈ 10 mK. By doing so, the spins carried by the copper nuclei get polarised. Then the heat switch is « opened », and the magnetic field is very slowly decreased down to B_fin. This process is adiabatic, which means that it takes place at constant disorder (entropy): the spins remain polarized, which means that the temperature has to decrease to T_fin. This is illustrated on the drawing below.

If the process is ideal, it verifies B_ini /B_fin = T_ini  /T_fin. Therefore, demagnetising down to 70 mT cools the system down to 100 µK. More information can be found in e.g. F. Pobell, Matter and Methods at Low Temperatures, Springer (2007).

One important component of cryogenics, besides cooling techniques, is thermometry. It is indeed mandatory to control what is the actual temperature of different places within the cryostat (including of course the sample!), and also to manage the heat loads. Obviously, the colder we are, the more difficult this task is. Above 4 K, one can use the electrical resistivity of a piece of metal (in this case, platinum) to work out the temperature. In the dilution temperature range (down to 10 mK), one can use non-metallic probes like carbon resistors which value will grow substantially as they cool. The measurement has to be done very reliably, at the lowest possible injected power (in order not to heat). This is performed using resistance bridges, connected with 4 wires to the probe. Below 10 mK, thermometry becomes very difficult. We use a home-made ³He thermometer: a quartz tuning fork immersed in the liquid that measures its viscosity. This is shown on the graph below.

The properties of ³He are well known and tabulated; this makes this device very reliable. ³He becomes superfluid below Tc ≈ 1 mK (BCS pairing of Fermions). Above this temperature, it is a Fermi liquid. More on thermometry can be found in e.g. F. Pobell, Matter and Methods at Low Temperatures, Springer (2007).

The Ultra-low temperature group works in close contact with the cryogenics team of Néel. We participate in new technological developments, like nuclear demagnetisation adapted to dry cryostats. Many other technological aspects are tackled by the team, like e.g. microwave optomechanics. As such, we possess a bunch of 4 K liquid helium cryostats, and many other mandatory pieces of equipment (noise SQUID thermometers, primary pressure gauges, lock-in detectors, …).

Microwave Optomechanics

Micro and nano electro-mechanical systems (MEMS and NEMS) can be actuated and detected by various means. Not relying on specific materials properties, the simplest are capacitive and magnetomotive schemes, which only require the device to be (at least partially) conducting.

For capacitive, the moving element is coupled to a gate electrode C on which a voltage V=V_dc+V_ac cos(ω t+Φ) is applied. Since the total capacitance C(x) depends on the motion x, this creates a force F= d/dx [1/2 C(x) V²] (which is usually non-linear, i.e. it depends on x). The motion can in turn be detected by the modulated current that flows through the capacitor, I = d/dt [C(x) V].

For magnetomotive, a current I=I_ac cos(ω t+Φ) is fed into the structure which is immersed in a static magnetic field B₀. A Laplace force then acts onto it F= I l_i B₀ (with l_i the length of the path taken by the current). This force is essentially linear, i.e. it does not depend on x. The motion of the conductor length l_i cuts the magnetic field lines which induces a voltage (Lenz law) V= – B₀ l_i d x/dt, which can be detected.

These techniques are rather straightforward, and require typically just a generator and a lock-in detector. However, because of the finite impedance of these apparatuses, the mechanical motion is usually loaded by the circuit: there is an extra damping acting on the mechanical resonance due to dissipation of energy in the electric circuit. As well, the resolution of these techniques is usually not very good; it is for instance impossible to resolve Brownian motion.

On the other hand, coupling moving objects to light is an extremely efficient way of actuating/detecting the motion: this is the field of optomechanics. One can detect Brownian motion, and the detection scheme is even quantum-limited (i.e. it reaches the ultimate limit fixed by Heisenberg’s uncertainty principle). But high intensity laser light is not very compatible with cryogenics; for this reason, microwave optomechanics is much more adapted.

The moving object is here coupled to an RLC circuit which acts as an optical cavity. The mechanical device modulates the capacitance C of the mode: this is a parametric coupling, i.e. the motion changes the resonance frequency of the microwave resonator. In practice, the cavity is coupled to a microwave transmission line, with one or two ports. It can thus be measured by sending a microwave signal into the line, and looking at the reflected/transmitted signal. This is what performs e.g. a Vector Network Analyser, see image above. More on microwaves can be found e.g. in D.M. Pozar, Microwave engineering, John Wiley and Sons (2012).

The modulation C(x) by the motion x(t) imprints sidebands in the measured spectrum. The simplest schemes that can be used are single-tone measurements, where a pump tone is applied at a frequency ω_cav+Δ (with ω_cav the microwave cavity resonance frequency) and Δ=0,+Ω_m,-Ω_m (with Ω_m the mechanical mode resonance frequency). The schematic below represents the case where the microwave cavity linewidth κ << Ω_m (so-called sideband resolved).

When the pump tone is applied at the cavity frequency (Δ=0), two equivalent sidebands appear on both sides, shifted by +-Ω_m. The peak area is directly linked to the energy stored in the mechanical mode, and its width is given by the mechanical damping rate Γ_m.

If now the pump tone is applied at Δ=-Ω_m (red detuned), the lower sideband (Stokes) is strongly suppressed and only the one at ω_cav is measured. This scheme allows to transfer energy from the mechanics to the optics: the mechanical mode can be (actively) cooled, and its damping Γ_eff is increased.

Reversely, when Δ=+Ω_m (blue detuned), the lower sideband is measured (and the Anti-Stokes suppressed). In this case, energy can flow from the optics to the mechanics, and the mode heats up (or equivalently, the motion is amplified). At the same time, the mechanical damping Γ_eff is reduced. For both red and blue detuned schemes, the efficiency of the cooling/heating depends on drive power through Γ_opt ∝ P_in.

On the graph above, we show an example of Brownian spectrum measured with blue detuned scheme at 200 mK on a 50 µm long SiN/Al beam device resonating around 4 MHz (cross-section 300×100 nm²). More on optomechanics can be found in M. Aspelmeyer, T.J. Kippenberg, F. Marquardt, Cavity Optomechanics: nano- and micromechanical resonators interacting with light, Springer (2013).

Training

As part of its duties, the ULT group is organizing Schools & Conferences over the years. The list can be found below, with extra information (use the links) like list of contributors/participants, and some available talks. A regular training session is the European Advanced Cryogenics School, which is organised today in the framework of the European Microkelvin Collaboration (EMP).

Cryocourse 2021 European Advanced Cryogenics School, Grenoble 2021

ULT 2014 Frontiers of low temperature physics, Bariloche (LT27 satellite conference)

Cryocourse 2013 European Advanced Cryogenics School, Grenoble 2013

Cryocourse 2011 European Advanced Cryogenics School, Grenoble 2011

Quantum Fluids and Solids QFS 2010 International Conference, Grenoble 2010

Cryocourse 2007 European Advanced Cryogenics School, Grenoble 2007

Workshop on Dark Matter Search and Related Topics Workshop JSPS-CNRS Collaboration, Grenoble 2007

Disorder and topological defects, a Helium primer COSLAB Workshop, Chamrousse 2004

Topological defects and the non-equilibrium dynamics of symmetry breaking phase transitions ESF Network and Winter school, Les Houches 1999

Workshop on the formation of topological defects ESF Network, Grenoble 1997

Funding

Within our Host Institution CNRS, our research is funded essentially by two main sources: these Funding Agencies are National (ANR), and mostly at the European level (ERC). Beyond the StG and CoG grants the group received, the ULT team is part of a European Infrastructure that federates Ultra-Low temperature physics (and technologies) at the European level.

ERC StG UNIGLASS (2017-2023): This European Starting grant is focused on the enigmatic universality found in low temperature properties of amorphous materials. The ultimate aim of this project is to be able to manipulate the quantum state of single low-energy states that are supposed to be at the origin of the unique properties of glasses (so-called Two-Level Systems).

H2020 infrastructure EMP (2019-2023): This is the Infrastructure grant that takes over Microkelvin (see below). The consortium is made of 17 partners, among which are 8 universities, 3 associated institutes, and 6 private companies. The eight European laboratories at the core of EMP all possess the capabilities to reach sub-milliKelvin temperatures; they are custodians of these technologies in Europe.

ERC CoG ULT-NEMS (2014-2021): In this Consolidator grant, following the ANR QNM project, the focus is on quantum properties probed by nano-mechancial resonators cooled down to ultra-low temperatures. Two aspects are dealt with: the microscopic scale (with elementary excitations from the surrounding baths that can couple to the mode under study), and the macroscopic one questioning basic concepts of Macroscopic Quantum Mechanics.

FRP7 Microkelvin (2009-2013): Infrastructure grant that links together all ultra-low temperature laboratories from Europe. CNRS Grenoble was one of the 3 founders of this consortium. This activity has been prolongated through EMP (see above).

 ANR MajoranaPRO (2013-2018): ANR project aiming at the study of exotic excitations present in superfluid ³He in confined conditions (so-called bound states). In particular, within the B-phase of the superfluid, these states are theoretically demonstrated to be Majorana (quasi-)particles.

ANR QNM (2010-2014): This ANR grant enabled to launch the ultra-cold MEMS and NEMS activity within the ULT team. The activity continued then within the ERC ULT-NEMS (see above).

ANR High-Q Fermions (2010-2014): This ANR research project aimed at studying elementary excitations in liquid helium with large Q wave-vector, by means of neutron spectroscopy.

ANR ULTIMA (2005-2008): ANR funded research project that evaluated the capabilities of ³He superfluid bolometers for the search of cold dark matter.

Data Management Publications

Experimental results published within the EMP consortium are published within green or gold open access. The data published is also made freely available to the interested readers:

To access these data, follow this link.

Cryogenics Database

Cryogenics Database (under construction).

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