We present a model to describe a generic circuit QED system which consists of multiple artificial three-level atoms, namely qutrits, strongly coupled to a cavity mode. When the state transition of the atoms disobey the selection rules the process that does not conserve the number of excitations can happen determinatively. Therefore, we can realize coherent exchange interaction among three or more atoms mediated by the exchange of virtual photons. In addition, we generalize the one cavity mode mediated interactions to the multi-cavity situation, providing a method to entangle atoms located in different cavities. Using experimental feasible parameters, we investigate the dynamics of the model including three cyclic-transition three-level atoms, for which the two lowest-energy levels can be treated as qubits. Hence, we have found that two qubits can jointly exchange excitation with one qubit in a coherent and reversible way. In the whole process, the population in the third level of atoms is negligible and the cavity photon number is far smaller than 1. Our model provides a feasible scheme to couple multiple distant atoms together, which may find applications in quantum information processing.
Compared with a qubit, a qutrit (i.e., three-level quantum system) has a larger Hilbert space and thus can be used to encode more information in quantum information processing and communication. Here, we propose a scheme to transfer an arbitrary quantum state between two flux qutrits coupled to two resonators. This scheme is simple because it only requires two basic operations. The state-transfer operation can be performed fast because of using resonant interactions only. Numerical simulations show that high-fidelity transfer of quantum states between the two qutrits is feasible with current c…
We present a way to create entangled states of two superconducting transmon qutrits based on circuit QED. Here, a qutrit refers to a three-level quantum system. Since only resonant interaction is employed, the entanglement creation can be completed within a short time. The degree of entanglement for the prepared entangled state can be controlled by varying the weight factors of the initial state of one qutrit, which allows the prepared entangled state to change from a partially entangled state to a maximally entangled state. Because a single cavity is used, only resonant interaction is employe…
We construct the positive invertible map of the mixed states of a single qutrit onto the states of two identical fermions. It is shown that using this one-to-one correspondence between qutrit states and states of two identical three-dimensional fermions (the unphysical odd dimension is picked for simplicity) one may attribute hidden entanglement to a single mixed state of qutrit.
The realization of cross-Kerr nonlinearity is an important task for many applications in quantum information processing. In this work, we propose a method for realizing cross-Kerr nonlinearity interaction between two superconducting coplanar waveguide resonators coupled by a three-level superconducting flux qutrit (coupler). By employing the qutrit-resonator dispersive interaction, we derive an effective Hamiltonian involving two-photon number operators and a coupler operator. This Hamiltonian can be used to describe a cross-Kerr nonlinearity interaction between two resonators when the coupler…
We present an efficient method to generate a Greenberger-Horne-Zeilinger (GHZ) entangled state of three cat-state qubits (cqubits) via circuit QED. The GHZ state is prepared with three microwave cavities coupled to a superconducting transmon qutrit. Because the qutrit remains in the ground state during the operation, decoherence caused by the energy relaxation and dephasing of the qutrit is greatly suppressed. The GHZ state is created deterministically because no measurement is involved. Numerical simulations show that high-fidelity generation of a three-cqubit GHZ state is feasible with prese…
We propose a scheme for the deterministic coherent manipulation of two atomic qutrits, trapped in separate cavities coupled through a short optical fibre or optical resonator. We study such a system in the regime of dispersive atom-field interactions, where the dynamics of atoms, cavities and fibre operates through virtual population of both the atomic excited states and photonic states in the cavities and fibre. We show that the resulting effective dynamics allows for the creation of robust qutrit entanglement, and thoroughly investigate the influence of imperfections and dissipation, due to …
Cat-state qubits (qubits encoded with cat states) have recently drawn intensive attention due to their enhanced life times with quantum error correction. We here propose a method to implement a universal controlled-phase gate of two cat-state qubits, via two microwave resonators coupled to a superconducting transmon qutrit. During the gate operation, the qutrit remains in the ground state; thus decoherence from the qutrit is greatly suppressed. This proposal requires only two basic operations and neither classical pulse nor measurement is needed; therefore the gate realization is simple. Numer…
The generation, manipulation and fundamental understanding of entanglement lies at very heart of quantum mechanics. Among various types of entangled states, the NOON states are a kind of special quantum entangled states with two orthogonal component states in maximal superposition, which have a wide range of potential applications in quantum communication and quantum information processing. Here, we propose a fast and simple scheme for generating NOON states of photons in two superconducting resonators by using a single superconducting transmon qutrit. Because only one superconducting qutrit a…
Compared with a qubit, a qudit (i.e., $d$-level or $d$-state quantum system) provides a larger Hilbert space to store and process information. On the other hand, qudit-based hybrid quantum computing usually requires performing hybrid quantum gates with qudits different in their nature or in their encoding format. In this work, we consider the qutrit case, i.e., the case for a qudit with $d$=3. We propose a simple method to realize a hybrid quantum controlled-SUM gate with one superconducting (SC) qutrit and a cat-state qutrit. This gate plus single-qutrit gates form a universal set of ternary …
We propose a method for transferring quantum entangled states of two photonic cat-state qubits (cqubits) from two microwave cavities to the other two microwave cavities. This proposal is realized by using four microwave cavities coupled to a superconducting flux qutrit. Because of using four cavities with different frequencies, the inter-cavity crosstalk is significantly reduced. Since only one coupler qutrit is used, the circuit resources is minimized. The entanglement transfer is completed with a single-step operation only, thus this proposal is quite simple. The third energy level of the co…
We present a way to transfer maximally- or partially-entangled states of n single-photon-state (SPS) qubits onto n coherent-state (CS) qubits, by employing 2n microwave cavities coupled to a superconducting flux qutrit. The two logic states of a SPS qubit here are represented by the vacuum state and the single-photon state of a cavity, while the two logic states of a CS qubit are encoded with two coherent states of a cavity. Because of using only one superconducting qutrit as the coupler, the circuit architecture is significantly simplified. The operation time for the state transfer does not i…
We propose a single-step implementation of a muti-target-qubit controlled phase gate with one cat-state qubit (\textit{cqubit}) simultaneously controlling $n-1$ target \textit{cqubits}. The two logic states of a \textit{cqubit} are represented by two orthogonal cat states of a single cavity mode. In this proposal, the gate is implemented with $n$ microwave cavities coupled to a superconducting transmon qutrit. Because the qutrit remains in the ground state during the gate operation, decoherence caused due to the qutrit's energy relaxation and dephasing is greatly suppressed. The gate implement…
We propose an efficient method to generate a GHZ entangled state of n photons in n microwave cavities (or resonators) via resonant interaction to a single superconducting qutrit. The deployment of a qutrit, instead of a qubit, as the coupler enables us to use resonant interactions exclusively for all qutrit-cavity and qutrit-pulse operations. This unique approach significantly shortens the time of operation which is advantageous to reducing the adverse effects of qutrit decoherence and cavity decay on fidelity of the protocol. Furthermore, the protocol involves no measurement on either the sta…
Qutrits (i.e., three-level quantum systems) can be used to achieve many quantum information and communication tasks due to their large Hilbert spaces. In this work, we propose a scheme to transfer an unknown quantum state between two flux qutrits coupled to two superconducting coplanar waveguide resonators. The quantum state transfer can be deterministically achieved without measurements. Because resonator photons are virtually excited during the operation time, the decoherences caused by the resonator decay and the unwanted inter-resonator crosstalk are greatly suppressed. Moreover, our appro…
We present a novel method to realize a multi-target-qubit controlled phase gate with one microwave photonic qubit simultaneously controlling $n-1$ target microwave photonic qubits. This gate is implemented with $n$ microwave cavities coupled to a superconducting flux qutrit. Each cavity hosts a microwave photonic qubit, whose two logic states are represented by the vacuum state and the single photon state of a single cavity mode, respectively. During the gate operation, the qutrit remains in the ground state and thus decoherence from the qutrit is greatly suppressed. This proposal requires onl…
We propose two schemes for generating the Knill-Lafamme-Milburn (KLM) states of two distant polar molecules (PMs) ensembles respectively in two transmission-line resonators (TLRs) connected by a superconducting charge qutrit (SCQ), and of two SCQs in a TLR, respectively. Both of the schemes are robust against photon decay due to the virtual excitations of the microwave photons of the TLRs, and the spontaneous emission can be suppressed owing to the virtual transitions of the SCQs in the second scheme. In addition, the schemes have high controllability and feasibility under the current availabl…
We propose a superconducting qutrit-resonator chain model, and analytically work out forms of its topological edge states. The existence of the zero-energy mode enables to generate a state transfer between two ends of the chain, accompanied with state flips of all intermediate qutrits, based on which $N$-body Greenberger-Horne-Zeilinger (GHZ) states can be generated with great robustness against disorders of coupling strengths. Three schemes of generating large-scale GHZ states are designed, each of which possesses the robustness against loss of qutrits or of resonators, meeting a certain perf…
We present a gauge invariant digitization of $(1+1)$d scalar quantum electrodynamics for an arbitrary spin truncation for qudit-based quantum computers. We provide a construction of the Trotter operator in terms of a universal qudit-gate set. The cost savings of using a qutrit based spin-1 encoding versus a qubit encoding are illustrated. We show that a simple initial state could be simulated on current qutrit based hardware using noisy simulations for two different native gate set.
The NOON states are valuable quantum resources, which have a wide range of applications in quantum communication, quantum metrology, and quantum information processing. Here we propose a fast, concise and reliable protocol for deterministically generating the NOON states of two resonators coupled to a single $\triangle$-type superconducting qutrit. In particular, we derive the effective Hamiltonians at the multi-photon resonances by virtue of the strong counter-rotating interaction between the resonator modes and the qutrit. Based on these crucial effective Hamiltonians, our protocol simplifie…
We present an efficient scheme for the generation of NOON states of photons in circuit QED assisted by a superconducting charge qutrit. It is completed with two kinds of manipulations, that is, the resonant operation on the qutrit and the resonator, and the single-qubit operation on the qutrit, and they both are high-fidelity operations. Compared with the one by a superconducting transmon qutrit proposed by Su et al. (Sci. Rep. 4, 3898 (2014)), our scheme does not require to maintain the qutrit in the third excited state with a long time, which relaxes the difficulty of its implementation in e…
We show that with the assistance of a third level of the qubits an n-qubit phase gate can be constructed from $2n-4$ two-qutrit conditional swap gates, a single qutrit-qubit controlled phase gate, and two single-qutrit operations. Unlike previous schemes, our scheme uses the auxiliary level to "expose" some state to the qutrit-qubit controlled phase gate, instead of using it to "hide" states from the conditional dynamics. Neither the number of the additional levels nor that of single-qutrit operations needs to increase with $n$. We propose a physical implementation of the required elementary g…
We consider the nonstationary circuit QED setup in which a 3-level artificial atom in the $Δ$-configuration interacts with a single-mode cavity field of natural frequency $ω$. It is demonstrated that when some atomic energy level(s) undergoes a weak harmonic modulation, photons can be generated from vacuum via effective 1- and 3-photon transitions, while the atom remains approximately in the ground state. These phenomena occur in the dispersive regime when the modulation frequency is accurately tuned near $ω$ and $3ω$, respectively, and the generated field states exhibit strikingly different s…
To generate a NOON state with a large photon number $N$, the number of operational steps could be large and the fidelity will decrease rapidly with $N$. Here we propose a method to generate a new type of quantum entangled states, $(|NN00\rangle+|00NN\rangle)/\sqrt{2}$ called "double NOON" states, with a setup of two superconducting flux qutrits and five circuit cavities. This scheme operates essentially by employing a two-photon process, i.e., two photons are simultaneously and separately emitted into two cavities when each coupler qutrit is initially in a higher-energy excited state. As a con…
Quantum reservoir engineering is a powerful framework for autonomous quantum state preparation and error correction. However, traditional approaches to reservoir engineering are hindered by unavoidable coherent leakage out of the target state, which imposes an inherent trade off between achievable steady-state state fidelity and stabilization rate. In this work we demonstrate a protocol that achieves trade off-free Bell state stabilization in a qutrit-qubit system realized on a circuit-QED platform. We accomplish this by creating a purely dissipative channel for population transfer into the ta…
Implementation of discrete-time quantum walk (DTQW) with superconducting qubits is difficult since on-chip superconducting qubits cannot hop between lattice sites. We propose an efficient protocol for the implementation of DTQW in circuit quantum electrodynamics (QED), in which only $N+1$ qutrits and $N$ assistant cavities are needed for an $N$-step DTQW. The operation of each DTQW step is very quick because only resonant processes are adopted. The numerical simulations show that high-similarity DTQW with the number of step up to $20$ is feasible with present-day circuit QED technique. This pr…
We propose a protocol to construct the 35 $f$-controlled phase gates of a three-qubit refined Deutsch-Jozsa (DJ) algorithm, by using single-qubit $σ_z$ gates, two-qubit controlled phase gates, and two-target-qubit controlled phase gates. Using this protocol, we discuss how to implement the three-qubit refined DJ algorithm with superconducting transmon qutrits resonantly coupled to a single cavity. Our numerical calculation shows that implementation of this quantum algorithm is feasible within the present circuit QED technique. The experimental realization of this algorithm would be an importan…
A single-photon switch is an important element for the building of scalable quantum networks. In this paper, we propose a feasible scheme for efficient single-photon switching. The proposed switch is controlled by a state of a qubit formed by the pair of the lowest levels of a three-level system (qutrit) coupled to a resonator. This resonator-qutrit system comprises a switching unit of the considered setup. For suppression of the Purcell relaxation of the control qubit, the switching unit is embedded into a coupled-resonator array serving as an engineered electromagnetic environment with a ban…
We present a one-step scheme to construct the controlled-phase gate deterministically on remote transmon qutrits coupled to different resonators connected by a superconducting transmission line for an universal distributed quantum computing. Different from previous works on remote superconducting qubits, the present gate is implemented with coherent evolutions of the entire system in the all-resonance regime assisted by the dark photons to robust against the transmission line loss, which allows the possibility of the complex designation of a long-length transmission line to link lots of circui…
We propose an efficient scheme for generating photonic NOON states of two resonators coupled to a four-level superconducting flux device. This proposal operates essentially by employing a technique of a coupler device resonantly interacting with two resonators simultaneously. As a consequence, the NOON-state preparation requires only $N+1$ operational steps and thus is much faster when compared with a recent proposal [Q. P. Su et al., Scientific Reports 4, 3898 (2014)] requiring $2N$ steps of operation. Moreover, due to the use of only two resonators and a device, the experimental setup is muc…
In quantum field theory, bare particles are dressed by a cloud of virtual particles to form physical particles. The virtual particles affect properties such as the mass and charge of the physical particles, and it is only these modified properties that can be measured in experiments, not the properties of the bare particles. The influence of virtual particles is prominent in the ultrastrong-coupling regime of cavity quantum electrodynamics (QED), which has recently been realized in several condensed-matter systems. In some of these systems, the effective interaction between atom-like transitio…
In this paper, we use the displacement operator together with parity operation to construct the superposition of two coherent states. By transmitting this superposition from 50-50 beam splitter the two-mode qubit like ECS is generated. Moreover, we introduce a controllable method for producing qutrit like ECS using atom-field interaction in cavity QED and beam splitter. We will show that the distances of peaks of Wigner functions for reduced density matrices of two-mode ECS's are entanglement sensitive and can be a witness for entanglement. To confirm the results we use concurrence measure to …
We report on a quantum electrodynamic (QED) investigation of the interaction between a ground state atom with another atom in an excited state. General expressions, applicable to any atom, are indicated for the long-range tails which are due to virtual resonant emission and absorption into and from vacuum modes whose frequency equals the transition frequency to available lower-lying atomic states. For identical atoms, one of which is in an excited state, we also discuss the mixing term which depends on the symmetry of the two-atom wave function (these evolve into either the gerade or the unger…
We show that a continuous-variable (CV) qudit can be constructed using quasiorthogonal cat states of a bosonic mode, when the phase encoded in each cat state is chosen appropriately. With the constructed CV qudit and the discrete-variable (DV) qudit encoded with Fock states, we propose an approach to generate the hybrid maximally entangled state of a CV qudit and a DV qudit by using two microwave cavities coupled to a superconducting flux qutrit. This proposal relies on the initial preparation of a superposition of Fock states of one cavity and the initial preparation of a cat state of the oth…
We present a way to realize a multiplex-controlled phase gate of n-1 control qubits simultaneously controlling one target qubit, with n qubits distributed in n different cavities. This multiqubit gate is implemented by using n qutrits (three-level natural or artificial atoms) placed in n different cavities, which are coupled to an auxiliary qutrit. Here, the two logic states of a qubit are represented by the two lowest levels of a qutrit placed in a cavity. We show that this n-qubit controlled phase gate can be realized using only 2n+2 basic operations, i.e., the number of required basic opera…
In a circuit consisting of two or more resonators, the inter-cavity crosstalk is inevitable, which could create some problems, such as degrading the performance of quantum operations and the fidelity of various quantum states. The focus of this work is to propose a crosstalk-insensitive method for simultaneously coupling multiple pairs of resonators, which is important in large-scale quantum information processing and communication in a network consisting of resonators or cavities. In this work, we consider 2N resonators of different frequencies, which are coupled to a three-level quantum syst…
With recent improvements in coherence times, superconducting transmon qubits have become a promising platform for quantum computing. They can be flexibly engineered over a wide range of parameters, but also require us to identify an efficient operating regime. Using state-of-the-art quantum optimal control techniques, we exhaustively explore the landscape for creation and removal of entanglement over a wide range of design parameters. We identify an optimal operating region outside of the usually considered strongly dispersive regime, where multiple sources of entanglement interfere simultaneo…
Stark shift on a superconducting qubit in circuit quantum electrodynamics (QED) has been used to construct universal quantum entangling gates on superconducting resonators in previous works. It is a second-order coupling effect between the resonator and the qubit in the dispersive regime, which leads to a slow state-selective rotation on the qubit. Here, we present two proposals to construct the fast universal quantum gates on superconducting resonators in a microwave-photon quantum processor composed of multiple superconducting resonators coupled to a superconducting transmon qutrit, that is,…
Provided that cavities are initially in a Greenberger-Horne-Zeilinger (GHZ) entangled state, we show that GHZ states of N-group qubits distributed in N cavities can be created via a 3-step operation. The GHZ states of the N-group qubits are generated by using N-group qutrits placed in the N cavities. Here, "qutrit" refers to a three-level quantum system with the two lowest levels representing a qubit while the third level acting as an intermediate state necessary for the GHZ state creation. This proposal does not depend on the architecture of the cavity-based quantum network and the way for co…
Hybrid quantum gates have recently drawn considerable attention. They play significant roles in connecting quantum information processors with qubits of different encoding and have important applications in the transmission of quantum states between a quantum processor and a quantum memory. In this work, we propose a single-step implementation of a multi-target-qubit controlled-NOT gate with one superconducting (SC) qubit simultaneously controlling $n$ target cat-state qubits. In this proposal, the gate is implemented with $n$ microwave cavities coupled to a three-level SC qutrit. The two logi…
We present a scheme to generate maximally entangled states of two three-level atoms with a nonresonant cavity by cavity-assisted collisions. Since the cavity field is only virtually excited no quantum information will be transferred from the atoms to the cavity.
We introduce and analyze theoretically a procedure that combines slow adiabatic STIRAP manipulation with short nonadiabatic Rabi pulses to produce any desired three-level state in a qutrit system. In this protocol, the fast pulses create superpositions between the ground state and the first excited state, while the slow pulses transfer an arbitrary population to the second excited state via stimulated Raman adiabatic passage (STIRAP). We demonstrate high-fidelity quantum control of the level populations and phases and we characterize the errors incurred under the breakdown of adiabaticity. In …
The exchange of virtual photons between quantum optical emitters in cavity QED or quantum nanophotonic setups induces interactions between them which can be harnessed for quantum information and simulation purposes. So far, these interactions have been mostly characterized for two-level emitters, which restrict their application to engineering quantum gates among qubits or simulating spin-1/2 quantum many-body models. Here, we show how to harness multi-level emitters with several optical transitions to engineer a wide class of photon-mediated interactions between effective spin-1 systems. We c…
Hybrid qubits have recently drawn intensive attention in quantum computing. We here propose a method to implement a universal controlled-phase gate of two hybrid qubits via two three-dimensional (3D) microwave cavities coupled to a superconducting flux qutrit. For the gate considered here, the control qubit is a microwave photonic qubit (particle-like qubit), whose two logic states are encoded by the vacuum state and the single-photon state of a cavity, while the target qubit is a cat-state qubit (wave-like qubit), whose two logic states are encoded by the two orthogonal cat states of the othe…
We propose a scheme to implement the $1\to2$ universal quantum cloning machine of Buzek et.al [Phys. Rev.A 54, 1844(1996)] in the context of cavity QED. The scheme requires cavity-assisted collision processes between atoms, which cross through nonresonant cavity fields in the vacuum states. The cavity fields are only virtually excited to face the decoherence problem. That's why the requirements on the cavity quality factor can be loosened.
In this paper, we introduce a controllable method for producing two and three-mode entangled coherent states (ECS's) using atom-field interaction in cavity QED and beam splitter. The generated states play central roles in linear optics, quantum computation and teleportation. We especially focus on qubit, qutrit and qufit like ECS's and investigate their entanglement by concurrence measure. Moreover, we illustrate decoherence properties of ECS's due to noisy channels, using negativity measure. At the end the effect of noise on monogamy inequality is discussed.
We introduce a scheme for perfect routing of quantum states and entanglement in regular cavity QED networks. The couplings between the cavities are quasi-uniform and each cavity is doped with a two-level atom. Quasi-uniform couplings leads the system to evolve in invariant subspaces. Combination the evolutions of the system in its invariant subspaces with quite simple local operations on atoms in the networks, gives the perfect routing of quantum states and entanglement through the network. To provide the protocol be robust due to decoherence arisen from photon loss, the field mode of the cavi…
We propose schemes to create cluster states and W states by many superconducting-quantum-interference-device (SQUID) qubits in cavities under the influence of the cavity decay. Our schemes do not require auxiliary qubits, and the excited levels are only virtually coupled throughout the scheme, which could much reduce the experimental challenge. We consider the cavity decay in our model and analytically demonstrate its detrimental influence on the prepared entangled states.
We present a scheme to achieve maximally entangled states, controlled phase-shift gate, and SWAP gate for two superconducting-quantum-interference-device (SQUID) qubits, by placing SQUIDs in a microwave cavity. We also show how to transfer quantum information from one SQUID qubit to another. In this scheme, no transfer of quantum information between the SQUIDs and the cavity is required, the cavity field is only virtually excited and thus the requirement on the quality factor of the cavity is greatly relaxed.
Higher-order transitions can occur in the ultrastrong-coupling regime of circuit QED through virtual processes governed by the counter-rotating interactions. We propose a feasible way to probe higher-order transitions through the scattering of propagating microwave photons incident on the hybrid qubit-cavity system. The lineshapes in the scattering spectra can indicate the coherent interaction between the qubits and the cavity, and the higher-order transitions can be identified in the population spectra. We further find that if the coupling strengths between the two qubits and the cavity are t…
I show a scheme which allows a perfect transfer of an unknown single-qubit atomic state from one atom to another by letting two atoms interact simultaneously with a cavity QED. During the interaction between atom and cavity, the cavity is only virtually excited and accordingly the scheme is insensitive to the cavity field states and cavity decay. Based on this scheme, a network for transfer of an arbitrary single-qubit atomic state between atoms is engineered. Then the scheme is generalized to perfectly transfer an arbitrary 2-qubit atomic state and accordingly a network for transfer of an arb…
A cavity QED implementation of the non-adiabatic holonomic quantum computation in decoherence-free subspaces is proposed with nitrogen-vacancy centers coupled commonly to the whispering-gallery mode of a microsphere cavity, where a universal set of quantum gates can be realized on the qubits. In our implementation, with the assistant of the appropriate driving fields, the quantum evolution is insensitive to the cavity field state, which is only virtually excited. The implemented non-adiabatic holonomies, utilizing optical transitions in the Λ type of three-level configuration of the nitrogen-v…
We propose to simulate dynamical phases of a BCS superconductor using an ensemble of cold atoms trapped in an optical cavity. Effective Cooper pairs are encoded via internal states of the atoms and attractive interactions are realized via the exchange of virtual photons between atoms coupled to a common cavity mode. Control of the interaction strength combined with a tunable dispersion relation of the effective Cooper pairs allows exploration of the full dynamical phase diagram of the BCS model, as a function of system parameters and the prepared initial state. Our proposal paves the way for t…
One-step implementation of a multi-target-qubit controlled-phase gate with photonic qubits encoded via eigenstates of the photon-number parity operator
Quantum optics with giant emitters has shown a new route for the observation and manipulation of non-Markovian properties in waveguide-QED. In this paper we extend the theory of giant atoms, hitherto restricted to the perturbative light-matter regime, to deal with the ultrastrong coupling regime. Using static and dynamical polaron methods we address the low energy subspace of a giant atom coupled to an Ohmic waveguide beyond the standard rotating wave approximation. We analyze the equilibrium properties of the system by computing the atomic frequency renormalization as a function of the coupli…
A macroscopic realization of the strange virtual particles is presented. The classical Helmholtz and the quantum mechanical Schrödinger equations are analogous differential equations. Their imaginary solutions are called evanescent modes in the case of elastic and electromagnetic fields. In the case of non-relativistic quantum mechanical fields they are called tunneling solutions. The imaginary solutions of this differential equation point to strange consequences: They are non local, they are not observable, and they described as virtual particles. During the last two decades QED calculations …
