We investigate the interaction of two two-level qubits with a single mode quantum field in a cavity without rotating wave approximation and considering that qubits can be located at an arbitrary distance from each other. We demonstrate that there exists a radiation induced interaction potential between atoms. We studied the properties of the system numerically and in addition constructed a simple analytical approximation. It is shown that the observable characteristics are substantially dependent on the distance between the qubits in the strong coupling regime. This allows one to perform the quantum control of the qubits, which can be exploited for the recording and transmission of quantum information.
We present a method for encoding second-quantized fermionic systems in qubits when the number of fermions is conserved, as in the electronic structure problem. When the number $F$ of fermions is much smaller than the number $M$ of modes, this symmetry reduces the number of information-theoretically required qubits from $Θ(M)$ to $O(F\log M)$. In this limit, our encoding requires $O(F^2\log^4 M)$ qubits, while encoded fermionic creation and annihilation operators have cost $O(F^2\log^5 M)$ in two-qubit gates. When incorporated into randomized simulation methods, this permits simulating time-evo…
In this letter we derive an expression for the force acting on a small (still macroscopic) particle in the field of the quantized electromagnetic radiation in any arbitrary quantum state. This result unifies in one simple formula all known expressions for the forces (i.e. van der Waals or frictional) acting on a small particle.
We present a novel approach for studying the dynamics of a superconducting qubit in a cavity. We succeed in linearizing the Hamiltonian through the application of an appropriate unitary transformation followed by a rotating wave approximation (RWA). For certain values of the parameters involved, we show that it is possible to obtain a a Jaynes-Cummings type Hamiltonian. As an example, we show the existence of super-revivals for the qubit inversion.
We report electromagnetically induced transparency using quantized fields in optomechanical systems. The weak probe field is a narrow band squeezed field. We present a homodyne detection of EIT in the output quantum field. We find that the EIT dip exists even though the photon number in the squeezed vacuum is at the single photon level. The EIT with quantized fields can be seen even at temperatures of the order of 100 mK paving the way for using optomechanical systems as memory elements.
The canonical quantization of flux is performed. It is shown that according to the canonical flux quantization there must be a new uncertainty relation: $e ΔA_m . Δx_m \geq \hbar$ where $A_m$ and $Δx_m \geq l_B$ are the electromagnetic gauge potential, the position uncertainty and the magnetic length, respectively. Other arguments in favour of this uncertainty relation are also discussed.
We study quantum dynamics of many-qubit systems strongly coupled to a quantized electromagnetic cavity mode, in the presence of decoherence and dissipation for both fermions and cavity photons. The analytic solutions are derived for a broad class of open quantum systems in Lindblad approximation. They include identical qubits, an ensemble of qubits with a broad distribution of transition frequencies, and multi-level electron systems. Compact analytic solutions for time-dependent quantum state amplitudes and observables become possible with the use of the stochastic equation of evolution for th…
The thermodynamical properties of a quantized electromagnetic field inside a box with perfectly conducting walls are studied using a regularization scheme that permits to obtain finite expressions for the thermodynamic potentials. The source of ultraviolet divergences is directly isolated in the expression for the density of modes, and the logarithmic infrared divergences are regularized imposing the uniqueness of vacuum and, consequently, the vanishing of the entropy in the limit of zero temperature. We thus obtain corrections to the Casimir energy and pressures, and to the specific heat that…
By using the Green-function concept of quantization of the electromagnetic field in dispersing and absorbing media, the quantized field in the presence of a dispersing and absorbing dielectric multilayer plate is studied. Three-dimensional input-output relations are derived for both amplitude operators in the ${\bf k}$-space and the field operators in the coordinate space. The conditions are discussed, under which the input-output relations can be expressed in terms of bosonic operators. The theory applies to both (effectively) free fields and fields, created by active atomic sources inside an…
The interaction of a quantized field with three-level atoms in $Λ$ configuration inside a two-mode cavity is analyzed in the small noise approximation. The atoms are in a two-photon detuning with respect to the carriers of the field. We calculate the stationary quadrature noise spectrum of the field outside the cavity in the case where the input probe field is a squeezed state and the input pump field is a coherent state. The mean value of the field is unaltered in all the analysis: the atoms shows electromagnetically induced transparency (EIT). The effect of the atoms' base level decoherence …
We study the scattering of the quantized electromagnetic field from a linear, dispersive dielectric using the scattering formalism for quantum fields. The medium is modeled as a collection of harmonic oscillators with a number of distinct resonance frequencies. This model corresponds to the Sellmeir expansion, which is widely used to describe experimental data for real dispersive media. The integral equation for the interpolating field in terms of the in field is solved and the solution used to find the out field. The relation between the in and out creation and annihilation operators is found…
The quantum behaviour of the electromagnetic field in mesoscopic elements is intimately linked to the quantization of the charge. In order to probe nonclassical aspects of the field in those elements, it is essential that thermal noise be reduced to the quantum level, i.e. to scales where kT < hν. This is easily achieved in dilution refrigerators for frequencies of a few GHz, i.e. in the microwave domain. Several recent experiments have highlighted the link between discrete charge transport and discrete photon emission in simple mesoscopic elements such as a tunnel junction. Photocount statist…
It is shown a complex function $Φ$ defined to be the product of a real Gaussian function and a complex Dirac delta function satisfies the Cauchy-Riemann equations. It is also shown these harmonic $Φ$-functions can be included in the solution of the classical electromagnetic field equations to generate the quantum field as a many-particle solution such that the $Φ$-functions represent the particle states. Creation and destruction operators are defined as usual to add or subtract photons from the particle states. The orbital angular momentum of the $Φ$-states is interpreted as spin since it emer…
We have developed a fully quantized model for EIT in which the decay rates are taken into account. In this model, the general form of the susceptibility and group velocity of the probe laser we obtained are operators. Their expectation value and fluctuation can be obtained on the Fock space. Furthermore the uncertainty of the group velocity under very weak intensity of the controlling laser and the uncertainty relation between the phase operator of coupling laser and the group velocity are approximately given. Considering the decay rates of various levels, we may analyze the probe laser near r…
A general theory of the interaction of the quantized electromagnetic field with atoms in the presence of dispersing and absorbing dielectric bodies of given Kramers--Kronig consistent permittivities is developed. It is based on a source-quantity representation of the electromagnetic field, in which the electromagnetic-field operators are expressed in terms of a continuous set of fundamental bosonic fields via the Green tensor of the classical problem. Introducing scalar and vector potentials, the formalism is extended in order to include in the theory the interaction of the quantized electroma…
We consider an approach in which the usual wave function in the quadrature representation of mode j of the electromagnetic field is further quantized to produce a field operator. Since the electromagnetic field is already second quantized, this corresponds to an additional or third quantization. The third-quantization approach can be used to perform certain quantum optics calculations in the Heisenberg picture that could only be performed in the Schrodinger picture when using the conventional second-quantized theory. This approach also allows an interesting generalization of quantum optics and…
The mechanism for entanglement of two flux qubits each interacting with a single mode electromagnetic field is discussed. By performing a Bell state measurements (BSM) on photons we find the two qubits in an entangled state depending on the system parameters. We discuss the results for two initial states and take into consideration the influence of decoherence.
A random field that is empirically equivalent to the quantized electromagnetic field is constructed. A mapping between the creation and annihilation operator algebras of a random field and of the quantized electromagnetic field provides a functor between the algebras and the Hilbert spaces generated by the vacuum states over those algebras. The functor inevitably does not extend to a functorial relationship between the local algebras generated by the random field and by the quantized electromagnetic field, but the empirical content provided by the vacuum state restores an empirical equivalence…
A quantized fermion can be represented by a scalar particle encircling a magnetic flux line. It has the spinor structure which can be constructed from quantum gates and qubits. We have studied here the role of Berry phase in removing dynamical phase during one qubit rotation of a quantized fermion. The entanglement of two qubit inserting spin-echo to one of them results the change of Berry phase that can be considered as a measure of entanglement. Some effort is given to study the effect of noise on the Berry phase of spinor and their entangled states.
In the paper an approach is presented allowing to model quantum logic circuits by electronic gates for discrete spatially modulated electromagnetic signals. The designed circuitry is for modeling low scale quantum nets of general design and quantum devices based only on superposition principle of their work.
We propose a method to measure the quantum state of a single mode of the electromagnetic field. The method is based on the interaction of the field with a probe qubit. The qubit polarizations along coordinate axes are functions of the interaction time and from their Fourier transform we can in general fully reconstruct pure states of the field and obtain partial information in the case of mixed states. The method is illustrated by several examples, including the superposition of Fock states, coherent states, and exotic states generated by the dynamical Casimir effect.
We study electromagnetically induced interference at superconducting qubits. The interaction between qubits and electromagnetic fields can provide additional coupling channels to qubit states, leading to quantum interference in a microwave driven qubit. In particular, the interwell relaxation or Rabi oscillation, resulting respectively from the multi- or single-mode interaction, can induce effective crossovers. The environment is modeled by a multi-mode thermal bath, generating the interwell relaxation. Relaxation induced interference, independent of the tunnel coupling, provides deeper unders…
The notion of the Trojan state of a Rydberg electron, introduced by I.Bialynicki-Birula, M.Kaliński, and J.H.Eberly (Phys. Rev. Lett. 73, 1777 (1994)) is extended to the case of the electromagnetic field quantized in acavity. The shape of the electronic wave packet describing the Trojan state is practically the same as in the previously studied externally driven system. The fluctuations of the quantized electromagnetic field around its classical value exhibit strong squeezing. The emergence of Trojan states in the cylindrically symmetrical system is attributed to spontaneous symmetry braking.
Electromagnetically induced transparency and absorption (EIT and EIA) are usually demonstrated by three-level atomic or atom-like systems. In contrast to the usual case, we theoretically study the EIT and EIA in an equivalent three-level system, which is constructed by dressing a superconducting two-level system (qubit) dressed by a single-mode cavity field. In this equivalent system, we find that both the EIT and the EIA can be tuned by controlling the level-spacing of the superconducting qubit and hence controlling the dressed system. This tunability is due to the dressed relaxation and deph…
We describe methods for simulating general second-quantized Hamiltonians using the compact encoding, in which qubit states encode only the occupied modes in physical occupation number basis states. These methods apply to second-quantized Hamiltonians composed of a constant number of interactions, i.e., linear combinations of ladder operator monomials of fixed form. Compact encoding leads to qubit requirements that are optimal up to logarithmic factors. We show how to use sparse Hamiltonian simulation methods for second-quantized Hamiltonians in compact encoding, give explicit implementations f…
Wave packet motion in a quantized electromagnetic field: Analytic results
ELI ALPS, The Extreme Light Infrastructure ERIC（ELI ALPS，极端光基础设施欧洲研究基础设施公司）；Department of Theoretical Physics, University of Szeged（塞格德大学理论物理系）；Bolyai Institute, University of Szeged（塞格德大学博莱研究所）；Department of Basic Sciences, Faculty of Mechanical Engineering and Automation, John von Neumann University（约翰·冯·诺依曼大学机械与自动化学院基础科学系）；Faculty of Physics, Babeş-Bolyai University（巴贝什-博约伊大学物理学院）
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 study linear and nonlinear optical properties of electromagnetically induced transparency (EIT) medium interacting with two quantized laser fields for adiabatic EIT case. We show that EIT medium exhibits normal dispersion. Kerr and higher order nonlinear refractive-index coefficients are also calculated in a completely analytical form. It is indicated that EIT medium exhibits giant resonantly enhanced nonlinearities. We discuss the response of the EIT medium to nonclassical light fields and find that the polarization vanishes when the probe laser is initially in a nonclassical state of no s…
A single 40Ca+ ion is trapped and laser cooled to its motional ground state. Laser radiation which couples off-resonantly to a motional sideband of the ion's S1/2 to D5/2 transition causes a phase shift proportional to the ion's motional quantum state |n>. As the phase shift is conditional upon the ion's motion, we are able to demonstrate a universal 2-qubit quantum gate operation where the electronic target state {S,D} is flipped depending on the motional qubit state |n>={|0>,|1>}. Finally, we discuss scaling properties of this universal quantum gate for linear ion crystals and present numeri…
We study the non-equilibrium dynamics of a pair of qubits made of two-level atoms separated in space with distance $r$ and interacting with one common electromagnetic field but not directly with each other. Our calculation makes a weak coupling assumption but no Born or Markov approximation. We write the evolution equations of the reduced density matrix of the two-qubit system after integrating out the electromagnetic field modes. We study two classes of states in detail: Class A is a one parameter family of states which are the superposition of the highest energy and lowest energy states, and…
We analyze Niels Bohr's proposed two-slit interference experiment with highly charged particles that argues that the consistency of elementary quantum mechanics requires that the electromagnetic field must be quantized. In the experiment a particle's path through the slits is determined by measuring the Coulomb field that it produces at large distances; under these conditions the interference pattern must be suppressed. The key is that as the particle's trajectory is bent in diffraction by the slits it must radiate and the radiation must carry away phase information. Thus the radiation field m…
In this work, starting from commutation relations between phase-space operators (in "first quantization") we define averaged creation and annihilation operators and show that they satisfy a simple, deformed commutation relation. By extending this relation to the quantized electromagnetic field, we determine the new vacuum state which has a non-zero component in standard occupied states. In addition we are led to non-linear de Broglie relations for photons, which appreciably depart from linearity only in the very-high-energy regime. The nonlinear Compton scattering that follows from these assum…
We introduce a generalized angular spectrum representation for quantized light beams. By using our formalism, we are able to derive simple expressions for the electromagnetic vector potential operator in the case of: {a)} time-independent paraxial fields, {b)} time-dependent paraxial fields, and {c)} non-paraxial fields. For the first case, the well known paraxial results are fully recovered.
We discuss decoherence due to electromagnetic fluctuations in charge qubits formed by two lateral quantum dots. We use an effective circuit model to evaluate correlations of voltage fluctuations in the qubit setup. These correlations allows us to estimate energy (T1) and phase (T2) relaxation times of the the qubit system. Our theoretical estimate of the quality factor due to dephasing by electromagnetic fluctuations yields values much higher than those found in recent experiments, indicating that other sources of decoherence play a dominant role.
We quantize the macroscopic electromagnetic field in a system of non-dispersive polarizable bodies moving at constant velocities possibly exceeding the Cherenkov threshold. It is shown that in general the quantized system is unstable and neither has a ground state nor supports stationary states. The quantized Hamiltonian is written in terms of quantum harmonic oscillators associated with both positive and negative frequencies, such that the oscillators associated with symmetric frequencies are coupled by an interaction term that does not preserve the quantum occupation numbers. Moreover, in th…
We study the non-equilibrium dynamics of a pair of qubits made of two-level atoms separated in space with distance r and interacting with one common electromagnetic field but not directly with each other. Our calculation makes a weak coupling assumption, but no Born or Markov approximation. We derived a non-Markovian master equation for the evolution of the reduced density matrix of the two-qubit system after integrating out the electromagnetic field modes. It contains a Markovian part with a Lindblad type operator and a nonMarkovian contribution, the physics of which is the main focus of this…
We examine the entanglement between two qubits, supposed to be remotely located and driven by independent quantized optical fields. No interaction is allowed between the qubits, but their degree of entanglement changes as a function of time. We report a collapse and revival of entanglement that is similar to the collapse and revival of single-atom properties in cavity QED.
We discuss level splitting and sideband transitions induced by a modulated coupling between a superconducting quantum circuit and a nanomechanical resonator. First, we show how to achieve an unconventional time-dependent longitudinal coupling between a flux (transmon) qubit and the resonator. Considering a sinusoidal modulation of the coupling strength, we find that a first-order sideband transition can be split into two. Moreover, under the driving of a red-detuned field, we discuss the optical response of the qubit for a resonant probe field. We show that level splitting induced by modulatin…
Covariant quantization of the electromagnetic field imposes the so-called gauge-fixing modification on the Lagrangian density. As a result of that, the total angular momentum operator receives at least one gauge-fixing-originated contribution, whose presence causes some confusion in the literature. The goal of this work is to discuss in detail why such a contribution, having no classical interpretation, is actually indispensable. For this purpose, we divide canonical and Belinfante-Rosenfeld total angular momentum operators into different components and study their commutation relations, their…
We introduce a simple model for electromagnetically induced transparency in which all fields are treated quantum mechanically. We study a system of three separated atoms at fixed positions in a one-dimensional multimode optical cavity. The first atom serves as the source for a single spontaneously emitted photon; the photon scatters from a three-level Lambda-configuration atom which interacts with a single-mode field coupling two of the atomic levels; the third atom serves as a detector of the total transmitted field. We find an analytical solution for the quantum dynamics. From the quantum am…
In near-field optics and optical tunneling theory, photon wave mechanics, i.e., the first quantized theory of the photon, allows us to address the spatial field localization problem in a flexible manner which links smoothly to classical electromagnetics. In this letter, photon wave mechanics is developed in a rigorous and unified way, based on which field quantization is obtained in a new way.
We study quantum dynamics of many-qubit systems strongly coupled to a quantized electromagnetic cavity field in the presence of decoherence and dissipation for both fermions and cavity photons, and taking into account the varying coupling strength of different qubits to the cavity field and the spread of their transition frequencies. Compact analytic solutions for time-dependent quantum state amplitudes and observables are derived for a broad class of open quantum systems in Lindblad approximation with the use of the stochastic Schroedinger equation approach. We show that depending on the init…
The reduced dynamics of an atomic qubit coupled both to its own quantized center of mass motion through the spatial mode functions of the electromagnetic field, as well as the vacuum modes, is calculated in the influence functional formalism. The formalism chosen can describe the entangled non-Markovian evolution of the system with a full account of the coherent back-action of the environment on the qubit. We find a slight increase in the decoherence due to the quantized center of mass motion and give a condition on the mass and qubit resonant frequency for which the effect is important. In op…
Free-electron interactions with laser-driven nanophotonic nearfields can quantize the electrons' energy spectrum and provide control over this quantized degree of freedom. We propose to use such interactions to promote free electrons as carriers of quantum information and find how to create a qubit on a free electron. We find how to implement the qubit's non-commutative spin-algebra, then control and measure the qubit state with a universal set of 1-qubit gates. These gates are within the current capabilities of femtosecond-pulsed laser-driven transmission electron microscopy. Pulsed laser dri…
The study of quantum heat transport in superconducting circuits is significant for further understanding the connection between quantum mechanics and thermodynamics, and for possible applications for quantum information. The first experimental realisations of devices demonstrating photonic heat transport mediated by a qubit have already been designed and measured. Motivated by the analysis of such experimental results, and for future experimental designs, we numerically evaluate the photonic heat transport of qubit-resonator devices in the linear circuit regime through electromagnetic simulati…
We report a theoretical study of the electromagnetic waves (EWs) propagation through an array of superconducting qubits, i.e. coherent two-level systems, embedded in a low-dissipative transmission line. We focus on the near-resonant case as the frequency of EWs $ω\simeq ω_q$, where $ω_q$ is the qubit frequency. In this limit we derive the effective dynamic nonlinear wave equation allowing one to obtain the frequency dependent transmission coefficient of EWs, $D(ω)$. In the linear regime and a relatively wide frequency region we obtain a strong resonant suppression of $D(ω)$ in both cases of a …
Quasi-periodically driven quantum systems are predicted to exhibit quantized topological properties, in analogy with the quantized transport properties of topological insulators. We use a single nitrogen-vacancy center in diamond to experimentally study a synthetic quantum Hall effect with a two-tone drive. We measure the evolution of trajectories of two quantum states, initially prepared at nearby points in synthetic phase space. We detect the synthetic Hall effect through the predicted overlap oscillations at a quantized fundamental frequency proportional to the Chern number, which character…
We study the entanglement of the superconducting charge qubit with the quantized electromagnetic field in a microwave cavity. It can be controlled dynamically by a classical external field threading the SQUID within the charge qubit. Utilizing the controllable quantum entanglement, we can demonstrate the dynamic process of the quantum storage of information carried by charge qubit. On the other hand, based on this engineered quantum entanglement, we can also demonstrate a progressive decoherence of charge qubit with quantum jump due to the coupling with the cavity field in quasi-classical stat…
In absence of currents and charges the quantized electromagnetic field can be described by wave functions which for each individual wave vector are normalized to one. The resulting formalism involves reducible representations of the Canonical Commutation Relations. The corresponding paradigm is a space-time filled with two-dimensional quantum harmonic oscillators. Mathematically, this is equivalent with two additional dimensions penetrated by the electromagnetic waves.
