We report coherent frequency conversion in the gigahertz range via three-wave mixing on a single artificial atom in open space. All frequencies involved are in vicinity of transition frequencies of the three-level atom. A cyclic configuration of levels is therefore essential, which we have realised with an artificial atom based on the flux qubit geometry. The atom is continuously driven at two transition frequencies and we directly measure the coherent emission at the sum or difference frequency. Our approach enables coherent conversion of the incoming fields into the coherent emission at a designed frequency in prospective devices of quantum electronics.For a long time research in experimental quantum optics focused on studying ensembles of natural atoms [1,2]. However, there have been huge advances in performing analogous quantum optics experiments using other systems [3][4][5]. In particular, superconducting artificial atoms are remarkably attractive to study quantum optics phenomena. The artificial atoms are nano-scale electronic circuits that can be fabricated using well established techniques and can therefore be easily scaled up to larger systems. Their energy levels can be engineered as desired, and strong coupling can be achieved with resonators and transmission lines [6][7][8][9]. This greater control of parameters allows one to reproduce quantum optics phenomena with improved clarity or even reach regimes, that are unattainable with natural atoms. For instance coherent population trapping [10], electromagnetically induced transparency [11,12], Autlers-Townes splitting [13][14][15][16][17], and quantum wave mixing [18] have been experimentally observed in superconducting threelevel systems [19][20][21][22][23]. Moreover, three-level atoms can be used to cool quantum systems [24,25], amplify microwave signals [26] and generate single or entangled pairs of photons [27] -important applications for future quantum networks. Here we investigate three-wave mixing, a nonlinear optical effect that can occur in cyclic threelevel atoms, which are lacking in nature [28], but can easily be realised with superconducting artificial atoms. The only suitable natural systems for the three-wave mixing are chiral molecular three-level systems without inversion symmetry [29]. However, these systems cannot be tuned in frequency. Different to Josephson junction based parametric three-wave mixing devices [30], that rely on mixing on a classical non-linearity, we implement here another method to generate three-wave mixing using a single cyclic or ∆-type artificial atom. This was considered theoretically in references [28,31].We directly measure the coherent emission of the cyclic three-level atom under two external drives corresponding to two atomic transitions. The emission occurs at a sin-gle mixed frequency (sum or difference). This emission is a corollary of coherent frequency conversion but inherently differs from classical frequency conversion [32,33] which would result in sidebands at the sum and difference frequencies. ...

Abstract.The upper critical field H c2 (T) of sintered pellets of the recently discovered MgB 2 superconductor was investigated by transport, ac susceptibility and dc magnetization measurements in magnetic fields up to 16 T covering a temperature range between T c ∼ 39 K and T = 3 K ∼ 0.1T c . The H c2 data from ac susceptibility are consistent with resistance data and represent the upper critical field of the major fraction of the investigated sample which increases up to H c2 (0) = 13 T at T = 0 corresponding to a coherence length of ξ o = 5.0 nm. A small fraction of the sample exhibits higher upper critical fields which were measured both resistively and by dc magnetization measurements. The temperature dependence of the upper critical field, H c2 (T), shows a positive curvature near T c and at intermediate temperatures indicating that MgB 2 is in the clean limit. The H c2 (T) dependence can be described within a broad temperature region 0. The recent discovery of superconductivity in MgB 2 [1] at temperatures as high as 40 K has stimulated considerable interest in this system. MgB 2 , which has a hexagonal AlB 2 structure, is a type IIsuperconductor. A significant boron isotope effect was observed [2] which is an indication for electronphonon mediated superconductivity in this compound. Magnetic parameters as the Ginsburg-Landau parameter κ = 26 [3] and the temperature dependence of the upper critical field H c2 (T) [3-6] were determined from transport and magnetization measurements [3][4][5][6][7]. So far, a complete H c2 (T) curve was reported for a MgB 2 wire sample showing a high residual resistivity ratio of about 25 [7]. In the present paper, the temperature dependence of the upper critical field of a sintered MgB 2 pellet was studied in magnetic fields up to 16 T in order to analyse the shape of H c2 (T) in the whole temperature range for a sample with a moderate residual resistivity ratio. Polycrystalline samples of MgB 2 were prepared by a conventional solid state reaction. A stoichiometric mixture of Mg and B was pressed into pellets. These pellets were wrapped in a Ta foil and sealed in a quartz vial. The samples were sintered at 950°C for two hours. Electrical resistance and the superconducting transition of a sample 5 mm in length with a cross-section of about 1 mm 2 (cut from the initially prepared pellet) were investigated in magnetic fields up to 16 T using the standard four probe method and current densities between 0.2 and 1 A/cm 2 . AC susceptibility and dc magnetization measurements were performed on other pieces from the same pellet in magnetic fields up to 9 T and 5 T, respectively. In Fig. 1a, the temperature dependence of the electrical resistance of the investigated sample is shown. The resistivity at 40 K and 300 K are about 6.4 µΩcm and 29 µΩcm, respectively, resulting in a residual resistance ratio (RRR) of approximately 4.5. The midpoint value of the normal-state resistivity of the superconducting transition at zero-magnetic field is 38.8 K. A similar T c value of T c =39,0 K was...

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