We propose periodically-modulated entangled states of light and show that they can be generated in two experimentally feasible schemes of nondegenerate optical parametric oscillator (NOPO): (i) driven by continuously modulated pump field; (ii) under action of a periodic sequence of identical laser pulses. We show that the time-modulation of the pump field amplitude essentially improves the degree of continuous-variable entanglement in NOPO. We develop semiclassical and quantum theories of these devices for both below- and above-threshold regimes. Our analytical results are in well agrement with numerical simulation and support a concept of time-modulated entangled states.
We analyse periodically modulated quantum systems with $SU(2)$ and $SU(1,1)$ symmetries. Transforming the Hamiltonian into the Floquet representation we apply the Lie transformation method, which allows us to classify all effective resonant transitions emerging in time-dependent systems. In the case of a single periodically perturbed system, we propose an explicit iterative procedure for the determination of the effective interaction constants corresponding to every resonance both for weak and strong modulation. For coupled quantum systems we determine the efficient resonant transitions appear…
We study the scattering of photons from periodically modulated quantum-optical systems. For excitation-number conserving quantum optical systems, we connect the analytic structure of the frequency-domain N-photon scattering matrix of the system to the Floquet decomposition of its effective Hamiltonian. Furthermore, it is shown that the first order contribution to the transmission or equal-time N-photon correlation spectrum with respect to the modulation frequency is completely geometric in nature i.e. it only depends on the Hamiltonian trajectory and not on the precise nature of the modulation…
Phenomena of electromagnetically induced transparency (PEIT) may be interpreted by the Autler-Townes Splitting (ATS), where the coupled states are split by the coupling laser field, or by the quantum destructive interference (QDI), where the atomic phases caused by the coupling laser and the probe laser field cancel. We propose modulated experiments to explore the PEIT in an alternative way by periodically modulating the coupling and the probe fields in a ?-type three-level system. Our analytical and numerical results rule out the ATS interpretation and show that the QDI interpretation is more…
We report measurements of time-frequency entangled photon pairs and heralded single photons at telecommunications wavelengths, generated using a periodically-poled, lithium niobate on insulator (LNOI) waveguide pumped optically by a diode laser. We achieve a high Coincidences-to-Accidentals Ratio (CAR) at high pair brightness, a low value of the conditional self-correlation function [$g^{(2)}$(0)], and high two-photon energy-time Franson interferometric visibility, which demonstrate the high quality of the entangled photon pairs and heralded single photons.
We have demonstrated a high-flux source of polarization-entangled photons using a type-II phase-matched periodically-poled KTP parametric downconverter in a collinearly propagating configuration. We have observed quantum interference between the single-beam downconverted photons with a visibility of 99% and a measured coincidence flux of 300/s/mW of pump. The Clauser-Horne-Shimony-Holt version of Bell's inequality was violated with a value of 2.711 +/- 0.017.
We report on specific signatures of squeezing for time-modulated light fields. We show that application of periodically-modulated driving fields instead of continuous wave fields drastically improves the degree of quadrature integral squeezing in an optical parametric oscillator. These results particularly allow for applications in time-resolved quantum communication protocols.
Using a rigorous quantum model a comprehensive study of physical properties of entangled photon pairs generated in spontaneous parametric down-conversion in chirped periodically-poled crystals is presented. Spectral, temporal, as well as spatial characteristics of photon pairs are analyzed. Spectral bandwidths, photon-pair flux, and entanglement area can be effectively controlled by chirping. Quantification of entanglement between photons in a pair is given. Splitting of entanglement area in the transverse plane accompanied by spectral splitting has been revealed. Using the model temperature d…
We propose a scheme for the generation of counterpropagating polarization-entangled photon pairs from a dual-periodically poled crystal. Compared with the usual forward-wave type source, this source, in the backward-wave way, has a much narrower bandwidth. With a 2-cm-long bulk crystal, the bandwidths of the example sources are estimated to be 3.6 GHz, and the spectral brightnesses are more than 100 pairs/(s GHz mW). Two concurrent quasi-phase-matched spontaneous parametric down-conversion processes in a single crystal enable our source to be compact and stable. This scheme does not rely on an…
We study theoretically the superfluidity and stability of a Bose-Einstein condensate (BEC) whose interatomic scattering length is periodically modulated with optical Feshbach resonance. Our numerical study finds that the properties of this periodic BEC are strongly influenced by the modulation strength. When the modulation strength is small, only the Bloch waves close to the Brillouin zone edge suffer both Landau and dynamical instabilities. When the modulation strength is strong enough, all Bloch waves become dynamically unstable. In other words, the periodic BEC loses its superfluidity compl…
In this paper, we address the issue of the generation of non-degenerate cross-polarization-entangled photon pairs using type-II periodically poled lithium niobate. We show that, by an appropriate engineering of the quasi-phase-matching grating, it is possible to simultaneously satisfy the conditions for two spontaneous parametric down-conversion processes, namely ordinary pump photon down-conversion to either extraordinary signal and ordinary idler paired photons, or to ordinary signal and extraordinary idler paired photons. In contrast to single type-II phase-matching, these two processes, wh…
We unveil nontrivial topological properties of zero-temperature magnetization plateau states in periodically modulated quantum spin chains under a uniform magnetic field. As positions of plateaus are uniquely determined by the modulation period of exchange couplings, we find that the topologically nontrivial plateau state can be characterized by a nonzero integer Chern number and has nontrivial edge excitations. Our study clarifies the topological origin of the well-known phenomena of quantized magnetization plateaus in one-dimensional quantum spin systems and relates the plateau state to the …
We investigate the influence of periodically time-modulated cavity frequency on the generation of atomic squeezed states for a collection of N two-level atoms confined in a non-stationary cavity with a moving mirror. We show that the two-photon character of the field generated from the vacuum state of field plays a significant role in producing the atomic or spin squeezed states. We further show that the maximum amount of persistent atomic squeezing is obtained for the initial cavity field prepared in the vacuum state.
We have generated a new type of biphoton state by cavity-enhanced down-conversion in a type-II phase-matched, periodically-poled KTiOPO_4 (PPKTP) crystal. By introducing a weak intracavity birefringence, the polarization-entangled output was modulated between the singlet and triplet states according to the arrival-time difference of the signal and idler photons. This cavity-enhanced biphoton source is spectrally bright, yielding a single-mode fiber-coupled coincidence rate of 0.7 pairs/s per mW of pump power per MHz of down-conversion bandwidth. Its novel biphoton behavior may be utilized in s…
This work deals with soliton solutions of the nonlinear Schroedinger equation with a diversity of nonlinearities. We solve the equation in a potential which oscillates in time between attractive and expulsive behavior, in the presence of nonlinearities which are modulated in space and time. Despite the presence of the periodically expulsive behavior of the potential, the results show that the nonlinear equation can support a diversity of localized excitations of the bright and dark type which are remarkably robust.
We consider a model of leaky quantum wire in three dimensions. The Hamiltonian is a singular perturbation of the Laplacian supported by a line with the coupling which is bounded and periodically modulated along the line. We demonstrate that such a system has a purely absolutely continuous spectrum and its negative part has band structure with an at most finite number of gaps. This result is extended also to the situation when there is an infinite number of the lines supporting the perturbations arranged periodically in one direction.
A growing number of experimental set-ups in cavity optomechanics exploit periodically driven fields. However, such set-ups are not amenable to analysis using simple, yet powerful, closed-form expressions of linearized optomechanics, which have provided so much of our present understanding of experimental optomechanics. In the present paper, we formulate a new method to calculate quantum noise spectra in modulated optomechanical systems, which we analyze, compare, and discuss with two other recently proposed solutions: we term these (i) frequency-shifted operators (ii) Floquet and (iii) iterati…
We theoretically report an analog of photon-assisted tunneling (PAT) in a periodically driven lattice array without a static biased potential by studying a three-channel waveguide system. This analog of PAT can be achieved by only periodically modulating the top waveguide and adjusting the distance between the bottom and its adjacent waveguide. It is numerically shown that the PAT resonances also exist in the five-channel waveguide system and probably exist in the waveguide arrays with other odd numbers of waveguides, but they will become weak as the number of waveguides increases. With origin…
Using free-fermionic techniques we study the entanglement entropy of a block of contiguous spins in a large finite quantum Ising chain in a transverse field, with couplings of different types: homogeneous, periodically modulated and random. We carry out a systematic study of finite-size effects at the quantum critical point, and evaluate subleading corrections both for open and for periodic boundary conditions. For a block corresponding to a half of a finite chain, the position of the maximum of the entropy as a function of the control parameter (e.g. the transverse field) can define the effec…
Physical systems in the time domain may exhibit analogous phenomena in real space, such as time crystals, time-domain Fresnel lenses, and modulational interference in a qubit. Here we report the experimental realization of time-domain grating using a superconducting qutrit in periodically modulated probe and control fields via two schemes: Simultaneous modulation and complementary modulation. Both experimental and numerical results exhibit modulated Autler-Townes (AT) and modulation-induced diffraction (MID) effects. Theoretical results also confirm that the peak positions of the interference …
This book chapter describes the dynamics of a modulated oscillator for resonant and nonresonant modulation. Two types of resonant modulation are considered: additive, with frequency close to the oscillator eigenfrequency, and parametric, with frequency close to twice the eigenfrequency. It is shown that relaxation of the oscillator is accompanied by quantum noise, which leads to a finite-width distribution over quantum states even for T=0. The quantum noise also leads to switching between coexisting vibrational states via transitions over the barrier in phase space. The switching mechanism, qu…
Strongly interacting topological states in multi-particle quantum systems pose great challenges to both theory and experiment. Recently, bound states of elementary spin waves (magnons) in quantum magnets have been experimentally observed in quantum Heisenberg chains comprising ultracold Bose atoms in optical lattices. Here, we explore a strongly interacting topological state called topological magnon bound-state in the quantum Heisenberg chain under cotranslational symmetry. We find that the cotranslational symmetry is the key to the definition of a topological invariant for multi-particle qua…
In this paper, we study periodically modulated $s=1/2$ spin chain in a linear gradient potential (LP) that is generated by an external magnetic field. In the absence of the LP, the system has topological states that exhibit a magnetization plateau for a uniform external magnetic field. These topological states have a finite integer Chern number and their stability is clarified by an equivalent spinless fermion system derived by a Jordan-Wigner transformation. We show that the LP, which is nothing but a constant electric field in the spinless fermion system, destabilizes the topological states,…
We investigate the creation of entangled states of bright light beams obeying the condition of strong Einstein-Podolsky-Rosen-like paradox criterion in time-modulated quantum dissipative dynamics. Having in view the generation of these states we propose a non-degenerate optical parametric oscillator(NOPO) driven by an amplitude-modulated pump field. We develop semi-classical and quantum theories of this device for all operational regimes concluding that, contrary to ordinary NOPO, the continuous-variable entanglement becomes approximately perfect for high level of modulation. Our analytical re…
We study the population trapping extensively in a periodically driven Rydberg pair. The periodic modulation of the atom-light detuning effectively suppresses the Rabi couplings and, together with Rydberg-Rydberg interactions, leads to the state-dependent population trapping. We identify a simple yet a general scheme to determine population trapping regions using driving induced resonances, the Floquet spectrum, and the inverse participation ratio. Contrary to the single atom case, we show that the population trapping in the two-atom setup may not necessarily be associated with level crossings …
The authors demonstrate a form of two-photon-counting interferometry by measuring the coincidence counts between single-photon-counting detectors at an output port of a Mach-Zehnder Interferometer (MZI) following injection of broad-band time-frequency-entangled photon pairs (EPP) generated from collinear spontaneous parametric down conversion into a single input port. Spectroscopy and refractometry are performed on a sample inserted in one internal path of the MZI by scanning the other path in length, which acquires phase and amplitude information about the samples linear response. Phase modul…
We study the dynamics of two ensembles of atoms (or equivalently, atomic clocks) coupled to a bad cavity and pumped incoherently by a Raman laser. Our main result is the nonequilibrium phase diagram for this experimental setup in terms of two parameters - detuning between the clocks and the repump rate. There are three main phases - trivial steady state (Phase I), where all atoms are maximally pumped, nontrivial steady state corresponding to monochromatic superradiance (Phase II), and amplitude-modulated superradiance (Phase III). Phases I and II are fixed points of the mean-field dynamics, wh…
We study an one-dimensional transverse field Ising model with additional periodically modulated real and complex fields. It is shown that both models can be mapped on a pseudo spin system in the k space in the aid of an extended Bogoliubov transformation. This allows us to introduce the geometric quantity, the Chern number, to identify the nature of quantum phases. Based on the exact solution, we find that the spatially modulated real and complex fields rearrange the phase boundaries from that of the ordinary Ising model, which can be characterized by the Chern numbers defined in the context o…
Pulse propagation is studied in an EIT medium with the control field having a periodically varying phase (chirp). Based both on numerical calculations and on an approximate approach neglecting absorption and nonadiabatic effects, it is shown that transparency occurs for probe pulses having a sufficiently narrow envelope and an appropriately suited chirp. For other chirped pulses the evolution of their spectra along a sample is studied. Using a projection method one can divide a pulse into a part for which the medium is transparent and a rest for which it is opaque.
We investigate optical nonlinear interactions in a dynamic environment by studying generation of photons in spontaneous parametric down conversion inside a nonlinear cavity where the optical path length is periodically modulated in time. We show that the temporal dynamics of the cavity modify the nonlinear interaction and the generated continuous variable time-frequency entangled bi-photon state evolves into a tunable discrete higher dimensional state in the non-adiabatic modulation regime where the modulation time scales are much faster than the photon lifetime. In this regime, the system mim…
Using the density matrix formalism, we prove an existence theorem of the periodic steady-state for an arbitrary periodically-driven system. This state has the same period as the modulated external influence, and it is realized as an asymptotic solution ($t$$\to$$+\infty$) due to relaxation processes. The presented derivation simultaneously contains a simple computational algorithm non-using both Floquet and Fourier theories, i.e. our method automatically guarantees a full account of all frequency components. The description is accompanied by the examples demonstrating a simplicity and high eff…
We suggest the generation of photon pairs in a thermally induced nonlinear periodically-poled silica fiber by spontaneous parametric down-conversion. Photons are generated directly in eigenstates of optical angular momentum. Photons in a pair can be entangled in these states as well as in frequencies. We identify suitable spatial and polarization modes giving an efficient nonlinear interaction. By changing the pump field properties both narrow- and broad-band down-converted fields can be obtained.
We analyze the dynamics of a superconducting qubit and the phenomenon of multiorder Rabi oscillations in the presence of a time-modulated external field. Such a field is also presented as a bichromatic field consisting of two spectral components, which are symmetrically detuned from the qubit resonance frequency. This approach leads to obtaining qualitative quantum effects beyond those for the case of monochromatic excitation of qubits. We calculate Floquet states and quasienergies of the composite system "superconducting qubit plus time-modulated field" for various resonant regimes. We analyz…
We consider a quantum system periodically driven with a strength which varies slowly on the scale of the driving period. The analysis is based on a general formulation of the Floquet theory relying on the extended Hilbert space. It is shown that the dynamics of the system can be described in terms of a slowly varying effective Floquet Hamiltonian that captures the long-term evolution, as well as rapidly oscillating micromotion operators. We obtain a systematic high-frequency expansion of all these operators. Generalizing the previous studies, the expanded effective Hamiltonian is now time-depe…
