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We demonstrate a hybrid architecture consisting of a quantum dot circuit coupled to a single mode of the electromagnetic field. We use single wall carbon nanotube based circuits inserted in superconducting microwave cavities. By probing the nanotube-dot using a dispersive read-out in the Coulomb blockade and the Kondo regime, we determine an electron-photon coupling strength which should enable circuit QED experiments with more complex quantum dot circuits.PACS numbers: 73.63.Fg An atom coupled to a harmonic oscillator is one of the most illuminating paradigms for quantum measurements and amplification [1]. Recently, the joint development of artificial two-level systems and high finesse microwave resonators in superconducting circuits has brought the realization of this model on-chip [2,3]. This "circuit Quantum Electro-Dynamics" architecture allows, at least in principle, to combine circuits with an arbitrary complexity. In this context, quantum dots can also be used as artificial atoms [4,5]. Importantly, these systems often exhibit many-body features if coupled strongly to Fermi seas, as epitomized by the Kondo effect. Combining such quantum dots with microwave cavities would therefore enable the study of a new type of coupled fermionicphotonic systems.Cavity quantum electrodynamics [6] and its electronic counterpart circuit quantum electrodynamics[1] address the interaction of light and matter in their most simple form i.e. down to a single photon and a single atom (real or artificial). In the field of strongly correlated electronic systems, the Anderson model follows the same purified spirit [7]. It describes a single electronic level with onsite Coulomb repulsion coupled to a Fermi sea. In spite of its apparent simplicity, this model allows to capture non-trivial many body features of electronic transport in nanoscale circuits. It contains a wide spectrum of physical phenomena ranging from resonant tunnelling and Coulomb blockade to the Kondo effect. Thanks to progress in nanofabrication techniques, the Anderson model has been emulated in quantum dots made out of two dimensional electron gas[8], C60 molecules [9] or carbone nanotubes [10]. Here, we mix the two above situations. We couple a quantum dot in the Coulomb blockade or in the Kondo regime to a single mode of the electromagnetic field and take a step further towards circuit QED experiments with quantum dots. * To whom correspondence should be addressed: kontos@lpa.ens. fr FIG. 1: a. Schematics of the quantum dot embedded in the microwave cavity. The transmitted microwave field has different amplitude and phase from the input field as a result of its interaction with the quantum dot inside the cavity. The quantum dot is connected to "wires" and capacitively coupled to a gate electrode in the conventional 3-terminal transport geometry. b. Scanning electron microscope (SEM) picture in false colors of the coplanar waveguide resonator. Both the typical coupling capacitance geometry of one port of the resonator and the 3-terminals geometry are visib...

Recent experiments with ultra-cold atoms have demonstrated the possibility of realizing experimentally fermionic superfluids with imbalanced spin populations. We discuss how these developments have shed a new light on a half-century old open problem in condensed matter physics, and raised new interrogations of their own.

We study three same spin state fermions of mass M interacting with a distinguishable particle of mass m in the unitary limit where the interaction has a zero range and an infinite s-wave scattering length. We predict an interval of mass ratio 13.384 < M/m < 13.607 where there exists a purely fourbody Efimov effect, leading to the occurrence of weakly bound tetramers without Efimov trimers.PACS numbers: 34.50. In a system of interacting particles, the unitary limit corresponds to a zero range s-wave interaction with infinite scattering length [1]. In particular, this excludes any finite energy two-body bound state. Interestingly, in the three-body problem, the Efimov effect may take place [2], leading to the occurrence of an infinite number of threebody bound states, with an accumulation point in the spectrum at zero energy. This effect occurs in a variety of situations, the historical one being the case of three bosons, as recently studied in a series of remarkable experiments with cold atoms close to a Feshbach resonance [3]. It can also occur in a system of two same spin state fermions of mass M and a particle of another species of mass m, in which case the fermions only interact with the third particle, with an infinite s-wave scattering length: An infinite number of arbitrarily weakly bound trimers then appears in this 2 + 1 fermionic problem if the mass ratio α = M/m is larger than α c (2; 1) ≃ 13.607 [2].The four-body problem has recently attracted a lot of interest [4]. The question of the existence of a four-body Efimov effect is however to our knowledge still open. We give a positive answer to this question, by investigating the 3 + 1 fermionic problem in the unitary limit. We explicitly solve Schrödinger's equation in the zero range model [2] and we determine the critical mass ratio to have a purely four-body Efimov effect in this system, that is without Efimov trimers.In the zero-range model, the Hamiltonian reduces to a non-interacting form, here in free spacewith m 1 = m 2 = m 3 = M and m 4 = m. The interactions are indeed replaced by contact conditions on the wavefunction, ψ(r 1 , r 2 , r 3 , r 4 ), where r i , i = 1, 2, 3 is the position of a fermion and r 4 is the position of the other species particle: At the unitary limit, for i = 1, 2, 3, there exist functions A i such thatwhen r i tends to r 4 for a fixed value of the i-4 centroid R i4 ≡ (M r i + mr 4 )/(m + M ) different from the positions of the remaining particles r k , k = i, 4. The wavefunction is also subject to the fermionic exchange symmetry with respect to the first three variables r i , i = 1, 2, 3.In what follows, we shall assume that there is no three-body Efimov effect, a condition that is satisfied by imposing M/m < α c (2; 1) ≃ 13.607. The eigenvalue problem Hψ = Eψ with the contact conditions in Eq. (2) is then separable in hyperspherical coordinates [5]. After having separated out the center of mass C of the system, one introduces the hyperradius, withm = (3M + m)/4 the average mass, and a set of here 8 hyperangles Ω whose e...

We revisit the problem of three identical bosons in free space, which exhibits a universal hierarchy of bound states (Efimov trimers). Modeling a narrow Feshbach resonance within a two-channel description, we map the integral equation for the three-body scattering amplitude to a one-dimensional Schrödinger-type single-particle equation, where an analytical solution of exponential accuracy is obtained. We give exact results for the trimer binding energies, the three-body parameter, the threshold to the three-atom continuum, and the recombination rate.

We examine the concept of universal quantized resistance in the AC regime through the fully coherent quantum RC circuit comprising a cavity (dot) capacitively coupled to a gate and connected via a single spin-polarized channel to a reservoir lead. As a result of quantum effects such as the Coulomb interaction in the cavity and global phase coherence, we show that the charge relaxation resistance Rq is identical for weak and large transmissions and it changes from h/2e 2 to h/e 2 when the frequency (times ) exceeds the level spacing of the cavity; h is the Planck constant and e the electron charge. For large cavities, we formulate a correspondence between the charge relaxation resistance h/e 2 and the Korringa-Shiba relation of the Kondo model. Furthermore, we introduce a general class of models, for which the charge relaxation resistance is universal. Our results emphasize that the charge relaxation resistance is a key observable to understand the dynamics of strongly correlated systems.The Landauer-Büttiker formula for coherent DC transport lies at the heart of modern electronics 1,2,3 and embodies one of the most dramatic predictions of modern condensed-matter physics: the perfect quantization, in steps of e 2 /h, of the maximum electrical conductance in one-dimensional metallic channels. It is universal insofar as one may validly neglect the disruptive influences of inelastic scattering processes within the transport process. An elementary explanation of the quantization views the constriction as an electron wave guide which has a non-zero resistance even though there are no impurities, because of the reflections occurring when a small number of propagating modes in the wave guide is matched to a large number of modes in the reservoirs 4,5 . This conductance quantization has been observed in various systems such as quantum Hall states 6 , quantum point contacts 7,8 , carbon nanotubes 9,10 and the helical edge liquid of topological insulators 11 . In this manuscript, we thoroughly investigate the AC regime and show that the charge relaxation resistance may be universally quantized; while the quantized resistance in the DC case requires a perfectly transmitted channel 12,13 , the charge relaxation resistance remains quantized regardless of the mode transmission. More specifically, we consider the quantum RC circuit of Fig. 1 in the context of spin-polarized electrons. Theoretically, the study of AC coherent transport was pioneered in a scattering approach by Büttiker, Prêtre and Thomas 14 where a universal charge relaxation resistance of R q = h/2e 2 was predicted 15 for a single-mode resistor; the factor 1/2 is purely of quantum origin and must be distinguished from spin effects. Coulomb blockade effects 16,17 were ignored and later they have been partially included in an Hartree-Fock theory 18 . The quantum mesoscopic RC circuit has been successfully implemented in a two-dimensional electron gas and the charge relaxation resistance R q = h/2e 2 was measured 19,20 . Our work completes the proof of the univers...

Using a Fermi-liquid approach, we provide a comprehensive treatment of the current and current noise through a quantum dot whose low-energy behavior corresponds to an SU͑N͒ Kondo model, focusing on the case N = 4 relevant to carbon nanotube dots. We show that for general N, one needs to consider the effects of higher-order Fermi-liquid corrections even to describe low-voltage current and noise. We also show that the noise exhibits complex behavior due to the interplay between coherent shot noise, and noise arising from interaction-induced scattering events. We also treat various imperfections relevant to experiments, such as the effects of asymmetric dot-lead couplings.ductance and the shot noise as well as details on their derivation. In Sec. V, we summarize our main results for the conductance and shot noise of a SU͑N͒ Kondo quantum dot, and conclude. II. MODEL DESCRIPTION A. Kondo HamiltonianWe give here a compact synopsis of the quantum-dot model we study and how it gives rise to Kondo physics. The dot connected to the leads is described by the following Anderson Hamiltonian 29 . ͑1͒ c L/R,k is the annihilation operator for an electron of spin =1...N and energy k = បv F k ͑measured from the Fermi energy F ͒ confined on the left/right lead. d is the electron operator of the dot and n = d † d the corresponding density. U denotes the charging energy, d the single-particle energy on the dot and t L/R denotes the tunneling-matrix elements from the dot to the left/right lead. The general case of asymmetric leads contacts is parametrized by t L = t cos , t R = t sin with = ͓0, / 2͔. = / 4 recovers the symmetric case. The rotation in the basis of leads electrons

In this paper, we present a theoretical investigation for the ground state of an impurity immersed in a Fermi sea. The molecular regime is considered where a two-body bound state between the impurity and one of the fermions is formed. Both interaction and exchange of the bound fermion take place between the dimer and the Fermi sea. We develop a formalism based on a two channel model allowing us to expand systematically the ground state energy of this immersed dimer with the scattering length a. Working up to order a 3 , associated to the creation of two particle-hole pairs, reveals the first signature of the composite nature of the bosonic dimer. Finally, a complementary variational study provides an accurate estimate of the dimer energy even at large scattering length.