Superconducting metamaterials for waveguide quantum electrodynamics

Mirhosseini, Mohammad; Kim, Eunjong; Ferreira, Vinicius S.; Kalaee, Mahmoud; Sipahigil, Alp; Keller, Andrew J.; Painter, Oskar

doi:10.1038/s41467-018-06142-z

Cited by 124 publications

(102 citation statements)

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“…This metamaterial is characterized by a photonic bandgap at low frequencies, with a band characterized by a lefthanded dispersion relation [19][20][21][22] and a dense set of modes at frequencies just above the bandgap, commensurate with superconducting qubit transition energies. A variety of superconducting metamaterials have been studied previously [23][24][25][26][27], including some systems with applications in microwave quantum optics [28,29] and quantum-limited amplification of microwave signals [30][31][32]. In our present work, the dense mode spectrum we implement is appealing for future applications for architectures of quantum simulators and entanglement generation [17], whereby the qubits could be tuned between the low-frequency bandgap and the left-handed region of the spectrum just above the bandgap.…”

Section: Introductionmentioning

confidence: 99%

Mode Structure in Superconducting Metamaterial Transmission-Line Resonators

et al. 2019

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Superconducting metamaterials are a promising resource for quantum information science. In the context of circuit QED, they provide a means to engineer on-chip, novel dispersion relations and a band structure that could ultimately be utilized for generating complex entangled states of quantum circuitry, for quantum reservoir engineering, and as an element for quantum simulation architectures.Here we report on the development and measurement at millikelvin temperatures of a particular type of circuit metamaterial resonator composed of planar superconducting lumped-element reactances in the form of a discrete left-handed transmission line (LHTL) that is compatible with circuit QED architectures. We discuss the details of the design, fabrication, and circuit properties of this system. As well, we provide an extensive characterization of the dense mode spectrum in these metamaterial resonators, which we conducted using both microwave transmission measurements and laser scanning microscopy (LSM). Results are observed to be in good quantitative agreement with numerical simulations and also an analytical model based upon current-voltage relationships for a discrete transmission line. In particular, we demonstrate that the metamaterial mode frequencies, spatial profiles of current and charge densities, and damping due to external loading can be readily modeled and understood, making this system a promising tool for future use in quantum circuit applications and for studies of complex quantum systems.

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Section: Introductionmentioning

confidence: 99%

Mode Structure in Superconducting Metamaterial Transmission-Line Resonators

et al. 2019

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“…In fact, band gaps where the density of states vanishes can emerge, so that spontaneous emission in that bath can be prevented, but still interactions between the emitters can be mediated by virtual processes via the common bath [7,8]. Experiments with atoms, quantum dots, or superconductors interacting with structured bath has renewed the interest in investigating these phenomena [9][10][11][12][13][14][15]. Other experimental scenarios involving cold atoms in optical lattices with state-dependent potentials are amenable to the same description, and thus the appearance of analogous phenomena have been predicted [16,17] and have recently been observed [18].…”

Section: Introductionmentioning

confidence: 99%

Effective many-body Hamiltonians of qubit-photon bound states

Shi

González-Tudela

et al. 2018

New J. Phys.

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Quantum emitters (QEs) coupled to structured baths can localize multiple photons around them and form qubit-photon bound states. In the Markovian or weak coupling regime, the interaction of QEs through these single-photon bound states is known to lead to effective many-body QE Hamiltonians with tuneable but yet perturbative interactions. In this work we study the emergence of such models in the non-Markovian or strong coupling regime in different excitation subspaces. The effective models for the non-Markovian regime with up to three excitations are characterized using analytical methods, uncovering the existence of doublons or triplon states. Furthermore, we provide numerical results for systems with multiple excitations and demonstrate the emergence of polariton models with optically tuneable interactions, whose many-body ground state exhibits a superfluid-Mott insulator transition.intuitive picture [21] is that the single-photon bound state acts as an off-resonant cavity mode that mediates interaction between the QEs. The strength and functional form of these interactions depend on the QE-bath coupling strength, detuning as well as the band-dispersion relation. Although, these interactions can be made relatively strong to overcome other dissipative mechanism, their predicted strength is ultimately limited by the Markovian conditions under which these effective description has been derived.In this work, we study the effective many-body Hamiltonians emerging when QEs couple to structured baths beyond the Markovian limit, and investigate to which point the dipole-dipole description survives in this regime. Furthermore, we study the consequences on the effective QE interactions of the emergence of multiphoton bound states, which were recently predicted in the single QE regime [15, 23-26], but whose impact in the multi QE situation has not yet been fully considered. Our analysis allows us to uncover qualitatively different interaction Hamiltonians, in which multi-photon bound states (doublons/triplons) hop from QE to the other, and analytically characterize them up to three excitations. With more excitations, we numerically characterize the emergent polariton models using density matrix renormalization group (DMRG), and show that their interactions can be controlled optically through the QE-bath interactions, allowing us to probe the quantum phase transition between superfluid and Mott insulator.This manuscript is organized as follows. In section 2, we explain the model that will be used throughout the paper and review the results in the Markovian limit to have them as reference for the next section. In section 3, we study the single excitation subspace, deriving an effective Hamiltonian to describe the dipole-dipole interaction for two and many QEs. In sections 4-6, we study the two-excitation subspace for both the two and many QE regimes. Since the phenomenology in this regime differs significantly from what is expected in a Markovian description, we use section 4 to explain the analytical tools we use to charact...

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“…For measurements, a coherent signal at frequency ωp is generated by a vector network analyzer (VNA) at room temperature and fed through attenuators (red squares) to the sample, which sits in a cryostat cooled to 20 mK to avoid thermal fluctuations affecting the experiment. The reflected signal passes a bandpass filter (BPF) and amplifiers, and is then measured with the VNA.abled many important quantum-optical experiments in 1D waveguide QED in superconducting circuits in the past decade [25,28,30,[33][34][35][36][37][38][39][40][41][42][43] and inspired a wealth of theoretical studies for this platform [25,33,. As shown in Fig.…”

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Large Collective Lamb Shift of Two Distant Superconducting Artificial Atoms

et al. 2019

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Virtual photons can mediate interaction between atoms, resulting in an energy shift known as a collective Lamb shift. Observing the collective Lamb shift is challenging, since it can be obscured by radiative decay and direct atom-atom interactions. Here, we place two superconducting qubits in a transmission line terminated by a mirror, which suppresses decay. We measure a collective Lamb shift reaching 0.8% of the qubit transition frequency and exceeding the transition linewidth. We also show that the qubits can interact via the transmission line even if one of them does not decay into it.Introduction. In 1947, when attempting to pinpoint the fine structure of the hydrogen atom, Lamb and Retherford [1] discovered a small energy difference between the levels 2S 1/2 and 2P 1/2 , which were thought to be degenerate according to Dirac's theory of electrons. This energy difference between the two levels can be understood when vacuum fluctuations are included in the picture, as was verified later by self-energy calculations in the framework of quantum field theory [2][3][4]. Briefly put, a hydrogen atom will emit photons which are instantaneously reabsorbed; while these "virtual" photons are not detectable by themselves, they leave their traces in the Lamb shift.The hydrogen atoms that Lamb and Retherford used for their experiment were obtained from molecular hydrogen through tungsten catalyzation. Since the conversion rate for this process was very low, the 2S 1/2 level was only populated in a few atoms. Hence, the observable effects of virtual photon processes were limited to selfinteraction; exchanges of virtual photons between atoms could not be detected. However, it was later realized that atom-atom interaction mediated by virtual photons also gives rise to an energy shift, referred to as a collective, or cooperative, Lamb shift [5][6][7][8][9]. The atom-atom interaction also underpins the collective decay known as Dicke superradiance [10,11].There are several obstacles impeding the experimental observation of the collective Lamb shift. The shift can be enhanced by using many atoms, but, if these atoms are too close together, direct atom-atom interactions (not via virtual photons) can obscure the effect. Furthermore, the interaction giving rise to the collective Lamb shift is relatively weak in three dimensions, and the shift can also be hidden by the radiative linewidth (e.g., due to the collective decay). Despite these obstacles, there have been a few experimental demonstrations of collective Lamb shifts: in xenon gas [12], iron nuclei [13], rubidium vapor [14], strontium ions [15], cold rubidium atoms [16], and potassium vapor [17]. Mostly, these experiments used developments in atomic trapping and cooling [18] that have enabled higher densities of atomic ensembles, leading to a strong coupling between atomic condensates and cavity fields [19,20]. An improved theoretical understanding [21-23] of collective Dicke states also aided some of the experiments.With the single exception of Ref.[15], these previous expe...

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Superconducting metamaterials for waveguide quantum electrodynamics

Cited by 124 publications

References 59 publications

Mode Structure in Superconducting Metamaterial Transmission-Line Resonators

Mode Structure in Superconducting Metamaterial Transmission-Line Resonators

Effective many-body Hamiltonians of qubit-photon bound states

Large Collective Lamb Shift of Two Distant Superconducting Artificial Atoms

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