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Quantum field theory is assumed to be gauge invariant. We show that for a Dirac field the assumption of gauge invariance impacts on the way the vacuum state is defined, and also that the conventional definition of the vacuum state must be modified to take into account the requirements of gauge invariance.

Few have had the impact of Professor Boris P. Stoicheff on atomic, molecular, and optical physics and in the fields of nonlinear optics and molecular spectroscopy, in particular. This paper recounts a few of his accomplishments in the generation of coherent radiation tunable in the VUV and the application of this short wavelength source to the spectroscopy of diatomic molecules, with emphasis on the rare gas dimers Ar 2 , Kr 2 , and Xe 2 . PACS No.: 33.20Ni

An ultraviolet photoelectron (PE) spectrometer apparatus that utilzes a tuneable 50 W CW CO2 laser as a directed heat source was used to study the vacuum pyrolysis of diazoacetophenone (1a) and its p-methyl, p-methoxy, p-chloro, and p-nitro analogues 1b, 1c, 1d, and 1e.

This chapter explains the most important fundamentals of vacuum physics, focusing on the macroscopic equation of state, the kinetic theory of gases, and the description of transport phenomena. The behavior of real gases differs more or less from ideal‐gas behavior, depending on the conditions of state. Due to the bond between its molecular particles, a solid or liquid substance occupies a certain volume hardly influenced by ambient conditions (temperature, pressure, etc.). However, a gas completely fills an available volume and shows a number of macroscopic properties: it has a temperature and exerts a temperature‐dependent pressure to the walls. Transport properties of a gas depends on macroscopic properties including the transmission of frictional force through the gas shear stress. The chapter also deals with saturation vapor pressure and evaporation rate. Thermodynamics provides a simple model to describe the temperature dependence of saturation vapor pressure.

Low electronic gap graphene nanoribbons (GNRs) are used for the fabrication of nanomaterial-based devices and, when isolated, for mono-molecular electronics experiences, for which a well-controlled length is crucial. Here, an on-surface chemistry protocol is monitored for producing long and well-isolated GNR molecular wires on an Au(111) surface. The two-step Ullmann coupling reaction is sequenced in temperature from 100 °C to 350 °C by steps of 50 °C, returning at room temperature between each step and remaining in ultrahigh vacuum conditions. After the first annealing step at 100 °C, the monomers self-organize into 2-monolayered nano-islands. Next, the Ullmann coupling reaction takes place in both 1st and 2nd layers of those nano-islands. The nano-island lateral size and shape are controlling the final GNR lengths. Respecting the above on-surface chemistry protocol, an optimal initial monomer coverage of ~1.5 monolayer produces isolated GNRs with a final length distribution reaching up to 50 nm and a low surface coverage of ~0.4 monolayer suitable for single molecule experiments. The on-surface synthesis of graphene nanoribbons with control over their length and final surface coverage is desirable for electronic applications. Here, the authors outline a protocol to produce long and isolated graphene nanoribbons on an Au(111) surface, achieving lengths of up coverage down to ~0.4 monolayer, of potential value for mono-molecular electronics. to 50 nm and a low surface coverage down to ~0.4 monolayer, of potential value for mono-molecular electronics.

The control of light-matter interaction at the most elementary level has become an important resource for quantum technologies. Implementing such interfaces in the THz range remains an outstanding problem. Here, we couple a single electron trapped in a carbon nanotube quantum dot to a THz resonator. The resulting light-matter interaction reaches the deep strong coupling regime that induces a THz energy gap in the carbon nanotube solely by the vacuum fluctuations of the THz resonator. This is directly confirmed by transport measurements. Such a phenomenon which is the exact counterpart of inhibition of spontaneous emission in atomic physics opens the path to the readout of non-classical states of light using electrical current. This would be a particularly useful resource and perspective for THz quantum optics. Strong light-matter coupling has been realized at the level of single atoms and photons throughout most of the electromagnetic spectrum, except for the THz range. Here, the authors report a THz-scale transport gap, induced by vacuum fluctuations in carbon nanotube quantum dot through the deep strong coupling of a single electron to a THz resonator.

Phonon lasers, which exploit coherent amplifications of phonons, are a means to explore nonlinear phononics, image nanomaterial structures and operate phononic devices. Recently, a phonon laser governed by dispersive optomechanical coupling has been demonstrated by levitating a nanosphere in an optical tweezer. Such levitated optomechanical devices, with minimal noise in high vacuum, can allow flexible control of large-mass objects without any internal discrete energy levels. However, it is challenging to achieve phonon lasing with levitated microscale objects because optical scattering losses are much larger than at the nanoscale. Here we report a nonlinear multi-frequency phonon laser with a micro-size sphere, which is governed by dissipative coupling. The active gain provided by a Yb3+-doped system plays a key role. It achieves three orders of magnitude for the amplitude of the fundamental-mode phonon lasing, compared with the passive device. In addition, nonlinear mechanical harmonics can emerge spontaneously above the lasing threshold. Furthermore, we observe coherent correlations of phonons for both the fundamental mode and its harmonics. Our work drives the field of levitated optomechanics into a regime where it becomes feasible to engineer collective motional properties of typical micro-size objects.Sufficient optical gain provided by Yb3+ doping allows phonon lasing from a levitated optomechanical system at the microscale, which exhibits strong mechanical amplitudes and nonlinear mechanical harmonics above the lasing threshold.

Controlling the motional degrees of isolated, single nanoparticles trapped within optical fields in a high vacuum are seen as ideal candidates for exploring the limits of quantum mechanics in a new mass regime. These systems are also massive enough to be considered for future laboratory tests of the quantum nature of gravity. Recently, the translational motion of trapped particles has been cooled to microkelvin temperatures, but controlling all the observable degrees of freedom, including their orientational motion, remains an important goal. Here we report the control and cooling of all the translational and rotational degrees of freedom of a nanoparticle trapped in an optical tweezer, accomplished by cavity cooling via coherent elliptic scattering. We reached temperatures in the range of hundreds of microkelvins for the translational modes and temperatures as low as 5 mK for the librational degrees of freedom. This work brings within reach applications in quantum science and the study of single isolated nanoparticles via imaging and diffractive methods, free of interference from a substrate.Optically trapped and levitated nanoparticles can be used to study macroscopic quantum effects, but fully controlling their motion is difficult. Now, all six roto-translational degrees of freedom have been cooled, although not to the quantum ground state.

Ultrafast control of current on the atomic scale is essential for future innovations in nanoelectronics. Extremely localized transient electric fields on the nanoscale can be achieved by coupling picosecond duration terahertz pulses to metallic nanostructures. Here, we demonstrate terahertz scanning tunnelling microscopy (THz-STM) in ultrahigh vacuum as a new platform for exploring ultrafast non-equilibrium tunnelling dynamics with atomic precision. Extreme terahertz-pulse-driven tunnel currents up to 10 7 times larger than steady-state currents in conventional STM are used to image individual atoms on a silicon surface with 0.3 nm spatial resolution. At terahertz frequencies, the metallic-like Si(111)-(7 × 7) surface is unable to screen the electric field from the bulk, resulting in a terahertz tunnel conductance that is fundamentally different than that of the steady state. Ultrafast terahertz-induced band bending and non-equilibrium charging of surface states opens new conduction pathways to the bulk, enabling extreme transient tunnel currents to flow between the tip and sample. Controlling electric currents on the atomic scale requires being able to handle the ultrafast timescales involved. Now, experiments have demonstrated the feasibility of terahertz scanning tunnelling microscopy as a method for doing just that.