Nanoscale thermal imaging of dissipation in quantum systems

Abstract

Energy dissipation is a fundamental process governing the dynamics of physical, chemical, and biological systems. It is also one of the main characteristics distinguishing quantum and classical phenomena. In condensed matter physics, in particular, scattering mechanisms, loss of quantum information, or breakdown of topological protection are deeply rooted in the intricate details of how and where the dissipation occurs. Despite its vital importance the microscopic behavior of a system is usually not formulated in terms of dissipation because the latter is not a readily measureable quantity on the microscale. Although nanoscale thermometry is gaining much recent interest [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] , the existing thermal imaging methods lack the necessary sensitivity and are unsuitable for low temperature operation required for study of quantum systems. Here we report a superconducting quantum interference nano-thermometer device with sub 50 nm diameter that resides at the apex of a sharp pipette and provides scanning cryogenic thermal sensing with four orders of magnitude improved thermal sensitivity of below 1 µK/Hz 1/2 . The non-contact non-invasive thermometry allows thermal imaging of very low nanoscale energy dissipation down to the fundamental Landauer limit [16][17][18] of 40 fW for continuous readout of a single qubit at 1 GHz at 4.2 K. These advances enable observation of dissipation due to single electron charging of individual quantum dots in carbon nanotubes and reveal a novel dissipation mechanism due to resonant localized states in hBN encapsulated graphene, opening the door to direct imaging of nanoscale dissipation processes in quantum matter. 2 Investigation of energy dissipation on the nanoscale is of major fundamental interest for a wide range of disciplines from biological processes, through chemical reactions, to energy-efficient computing [1][2][3][4][5] . Study of dissipation mechanisms in quantum systems is of particular importance because dissipation demolishes quantum information. In order to preserve a quantum state the dissipation has to be extremely weak and hence hard to measure. As a figure of merit for detection of low power dissipation in quantum systems 16 we consider an ideal qubit operating at a typical readout frequency of 1 GHz. Landauer's principle states the lowest bound on energy dissipation in an irreversible qubit operation to be 0 = B ln 2, where B is Boltzmann's constant and is the temperature 17,18 . At = 4.2 K, 0 = 410 -23 J, several orders of magnitude below 10 -19 J of dissipation per logical operation in present day superconducting electronics and 10 -15 J in CMOS devices 19,20 . Hence the power dissipated by an ideal qubit operating at a readout rate of = 1 GHz will be as low as = 0 = 40.2 fW. The resulting temperature increase of the qubit will depend on its size and the thermal properties of the substrate. For example, a 120 × 120 nm 2 device on a 1 µm thick SiO 2 /Si substrate dissipating 40 fW will heat up by about 3 µK (Fig. 1). Suc...

Resonant electron-lattice cooling in graphene

“…Since the thickness of the graphene/hBN system is about 50 nm, which corresponds to about 150 atomic layers, this value of Z is physically reasonable. We also note that LS ≈ −22 meV agrees with the energy of a defect formed by a hydrogen adatom [18]. This highlights the use of resonance cooling as a way to identify the nature of a defect.…”

“…Recently impurity-assisted electron-lattice cooling in graphene was imaged using the nanoscale thermometry scanning probe technique [18,19]. It was found that the dominant contribution to cooling arises from resonant scatterers with the energies of the resonances positioned near the Dirac point.…”

“…While this picture seems plausible, the study reported in Refs. [18,19] left a number of key questions unanswered, in particular the origin of the resonances and the extent to which resonant scattering can enhance the cooling rates. Below we present a microscopic picture of cooling due to phonon emission mediated by resonant scattering, and estimate the cooling rate by evaluating the electronic cooling cross section.…”

Dynamics and heat diffusion of Abrikosov’s vortex-antivortex pairs during an annihilation process

“…Thus, conceivably, the annihilation of Abrikosov's V-AV pairs can be detected by measuring the magnetization response of the sample as a function of time, what would require fast and sensitive detection scheme. Another interesting aspect is that the local increase of the temperature in the annihilation is of the order of 10 −3 T c , which can be measured by a SQUID thermal sensor as described by Halbertal et al [58].…”

“…On the other hand, since W ψ is due to the relaxation of ψ, a narrower region is dominated by this dissipation mechanism. Recently, Halbertal and coworkers have shown to be possible imaging thermal dissipation in nanoscopic systems by using nanoSQUIDs [58]. Then, our theoretical approach should be experimentally confirmed since ∆T is of the order of 10…”