Thermal Transport in Nanoelectronic Devices Cooled by On-Chip Magnetic Refrigeration.

On-chip demagnetization refrigeration has recently emerged as a powerful tool for reaching microkelvin electron temperatures in nanoscale structures. The relative importance of cooling on-chip and off-chip components and the thermal subsystem dynamics are yet to be analyzed. We study a Coulomb blockade thermometer with on-chip copper refrigerant both experimentally and numerically, showing that dynamics in this device are captured by a first-principles model. Our work shows how to simulate thermal dynamics in devices down to microkelvin temperatures, and outlines a recipe for a low-investment platform for quantum technologies and fundamental nanoscience in this novel temperature range.

Nonlinear two-level dynamics of quantum time crystals.

A time crystal is a macroscopic quantum system in periodic motion in its ground state. In our experiments, two coupled time crystals consisting of spin-wave quasiparticles (magnons) form a macroscopic two-level system. The two levels evolve in time as determined intrinsically by a nonlinear feedback, allowing us to construct spontaneous two-level dynamics. In the course of a level crossing, magnons move from the ground level to the excited level driven by the Landau-Zener effect, combined with Rabi population oscillations. We demonstrate that magnon time crystals allow access to every aspect and detail of quantum-coherent interactions in a single run of the experiment. Our work opens an outlook for the detection of surface-bound Majorana fermions in the underlying superfluid system, and invites technological exploitation of coherent magnon phenomena - potentially even at room temperature.

Suppressing the Kibble-Zurek Mechanism by a Symmetry-Violating Bias.

The formation of topological defects in continuous phase transitions is driven by the Kibble-Zurek mechanism. Here we study the formation of single- and half-quantum vortices during transition to the polar phase of ^{3}He in the presence of a symmetry-breaking bias provided by the applied magnetic field. We find that vortex formation is suppressed exponentially when the length scale associated with the bias field becomes smaller than the Kibble-Zurek length. We thus demonstrate an experimentally feasible shortcut to adiabaticity-an important aspect for further understanding of phase transitions as well as for engineering applications such as quantum computers or simulators.

AC Josephson effect between two superfluid time crystals.

Quantum time crystals are systems characterized by spontaneously emerging periodic order in the time domain1. While originally a phase of broken time translation symmetry was a mere speculation2, a wide range of time crystals has been reported3-5. However, the dynamics and interactions between such systems have not been investigated experimentally. Here we study two adjacent quantum time crystals realized by two magnon condensates in superfluid 3He-B. We observe an exchange of magnons between the time crystals leading to opposite-phase oscillations in their populations-a signature of the AC Josephson effect6-while the defining periodic motion remains phase coherent throughout the experiment. Our results demonstrate that time crystals obey the general dynamics of quantum mechanics and offer a basis to further investigate the fundamental properties of these phases, opening pathways for possible applications in developing fields, such as quantum information processing.

Fundamental dissipation due to bound fermions in the zero-temperature limit.

The ground state of a fermionic condensate is well protected against perturbations in the presence of an isotropic gap. Regions of gap suppression, surfaces and vortex cores which host Andreev-bound states, seemingly lift that strict protection. Here we show that in superfluid 3He the role of bound states is more subtle: when a macroscopic object moves in the superfluid at velocities exceeding the Landau critical velocity, little to no bulk pair breaking takes place, while the damping observed originates from the bound states covering the moving object. We identify two separate timescales that govern the bound state dynamics, one of them much longer than theoretically anticipated, and show that the bound states do not interact with bulk excitations.

Bose-Einstein Condensation of Magnons and Spin Superfluidity in the Polar Phase of

The polar phase of ^{3}He, which is topological spin-triplet superfluid with the Dirac nodal line in the spectrum of Bogoliubov quasiparticles, has been recently stabilized in a nanoconfined geometry. We pump magnetic excitations (magnons) into the sample of polar phase and observe how they form a Bose-Einstein condensate, revealed by coherent precession of the magnetization of the sample. Spin superfluidity, which supports this coherence, is associated with the spontaneous breaking of U(1) symmetry by the phase of precession. We observe the corresponding Nambu-Goldstone boson and measure its mass emerging when applied rf field violates the U(1) symmetry explicitly. We suggest that the magnon BEC in the polar phase is a powerful probe for topological objects such as vortices and solitons and topological nodes in the fermionic spectrum.

Observation of a Time Quasicrystal and Its Transition to a Superfluid Time Crystal.

We report experimental realization of a quantum time quasicrystal and its transformation to a quantum time crystal. We study Bose-Einstein condensation of magnons, associated with coherent spin precession, created in a flexible trap in superfluid ^{3}He-B. Under a periodic drive with an oscillating magnetic field, the coherent spin precession is stabilized at a frequency smaller than that of the drive, demonstrating spontaneous breaking of discrete time translation symmetry. The induced precession frequency is incommensurate with the drive, and hence, the obtained state is a time quasicrystal. When the drive is turned off, the self-sustained coherent precession lives a macroscopically long time, now representing a time crystal with broken symmetry with respect to continuous time translations. Additionally, the magnon condensate manifests spin superfluidity, justifying calling the obtained state a time supersolid or a time supercrystal.

Observation of Half-Quantum Vortices in Topological Superfluid

One of the most sought-after objects in topological quantum-matter systems is a vortex carrying half a quantum of circulation. They were originally predicted to exist in superfluid ^{3}He-A but have never been resolved there. Here we report an observation of half-quantum vortices (HQVs) in the polar phase of superfluid ^{3}He. The vortices are created with rotation or by the Kibble-Zurek mechanism and identified based on their nuclear magnetic resonance signature. This discovery provides a pathway for studies of unpaired Majorana modes bound to the HQV cores in the polar-distorted A phase.

Light Higgs channel of the resonant decay of magnon condensate in superfluid (3)He-B.

In superfluids the order parameter, which describes spontaneous symmetry breaking, is an analogue of the Higgs field in the Standard Model of particle physics. Oscillations of the field amplitude are massive Higgs bosons, while oscillations of the orientation are massless Nambu-Goldstone bosons. The 125 GeV Higgs boson, discovered at Large Hadron Collider, is light compared with electroweak energy scale. Here, we show that such light Higgs exists in superfluid (3)He-B, where one of three Nambu-Goldstone spin-wave modes acquires small mass due to the spin-orbit interaction. Other modes become optical and acoustic magnons. We observe parametric decay of Bose-Einstein condensate of optical magnons to light Higgs modes and decay of optical to acoustic magnons. Formation of a light Higgs from a Nambu-Goldstone mode observed in (3)He-B opens a possibility that such scenario can be realized in other systems, where violation of some hidden symmetry is possible, including the Standard Model.

Self-trapping of magnon Bose-Einstein condensates in the ground state and on excited levels: from harmonic to box confinement.

Long-lived coherent spin precession of (3)He-B at low temperatures around 0.2T(c) is a manifestation of Bose-Einstein condensation of spin-wave excitations or magnons in a magnetic trap which is formed by the order-parameter texture and can be manipulated experimentally. When the number of magnons increases, the orbital texture reorients under the influence of the spin-orbit interaction and the profile of the trap gradually changes from harmonic to a square well, with walls almost impenetrable to magnons. This is the first experimental example of Bose condensation in a box. By selective rf pumping the trap can be populated with a ground-state condensate or one at any of the excited energy levels. In the latter case the ground state is simultaneously populated by relaxation from the exited level, forming a system of two coexisting condensates.