Fourth-order Squeezing Research Articles

Experimental preparation of generalized cat states for itinerant microwave photons

Generalized cat states represent arbitrary superpositions of coherent states, which are of great importance in various quantum information processing protocols. Here we demonstrate a versatile approach to creating generalized itinerant cat states in the microwave domain, by reflecting coherent-state photons from a microwave cavity containing a superconducting qubit. We show that with a coherent control of the qubit state, a full control over the coherent-state superposition can be realized. The prepared cat states are verified through quantum state tomography of the qubit-state-dependent reflection photon field. We further quantify quantum coherence in the prepared cat states based on the resource theory, revealing a good experimental control on the coherent-state superpositions. The photon number statistic and the squeezing properties are also analyzed. Remarkably, fourth-order squeezing is observed in the experimental states. Those results open up new possibilities of applying generalized cat states for the purpose of quantum information processing.

Non-classicalities exhibited by the superposition of Schrödinger’s cat state with the vacuum of the optical field

Superposition of two coherent states, the Schrodinger’s cat state, can exhibit different nonclassical properties having foundational applications in quantum information processing. We consider the ‘superposition of Schrodinger’s cat state with the vacuum state (SCVS)’ of the optical field. We discuss different witness of nonclassicality properties such as lower- and higher-order squeezing (viz., squeezing, Hong & Mandel’s fourth-order squeezing, amplitude-squared squeezing) and sub-Poissonian photon statistics. Further, we discuss the negativity of the Wigner function of SCVS indicating the nonclassicality of the state under investigation. We find that the vacuum state contribution in SCVS exhibits different nonclassicalities under some conditions stronger where the nonclassicalities exhibited by the state without vacuum state contribution are weaker.

Hong and Mandel fourth-order squeezing generated by the beam splitter with third-order nonlinearity from the coherent light

We study about the generation of Hong and Mandel fourth-order squeezing by the beam splitter with the third-order nonlinearity. We find that when we mix coherent light beam (a state which lies at the boundary of classical to non-classical region), we find situations where the output beam exhibit Hong and Mandel fourth-order squeezing.

Coherent population trapping based atomic reservoir for almost perfect higher-order squeezing.

Due to either coherent or dissipative interactions with the coherent population trapping (CPT)-based atoms, the evolutions of the Bogoliubov modes towards the vacuum states have been shown to lead to second-order squeezing of the involved optical fields. Here we push the CPT-based dissipative interactions towards higher-order squeezing, which is not simply determined by second-order squeezing but instead by different criteria involving higher-order moments. It is shown that the CPT-based atomic reservoir supports the dissipative evolution of the Bogoliubov modes almost completely to the vacuum states and then yields almost perfect fourth-order squeezing (90%∼100%). The present mechanism is robust against spontaneous emission since the atoms stay largely in the ground states. As a by-product, a comparison is given with two-level atoms, in which the excitation of a large fraction reduces the degree of higher-order squeezing.

Effects on squeezing and sub-poissonian of light in fourth harmonic generation up to first-order Hamiltonian interaction

The effects on squeezing and sub-poissonian of light in fourth harmonic generation (FHG) are investigated based on the fully quantum mechanically up to the first order Hamiltonian interaction in gt, where g is the coupling constant between the modes per second and t is the interaction time between the waves during the process in a nonlinear medium. FHG is a process in which an incident laser beam of the fundamental frequency ω interacts with a nonlinear medium to produce the harmonic frequency at 4ω. The coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators are established. The occurrence of amplitude squeezing effects in both the quadratures of the radiation field in the fundamental mode is investigated and found to be dependent on the selective phase values of the field amplitude. The photon statistics of the pump mode in this process have also been investigated and found to be sub-poissonian in nature. It is found that there is no possibility to produce squeezed light in the harmonic mode up to first-order interaction in gt. Further, we have found the case up to second-order Hamiltonian interaction in gt that the normal squeezing in the harmonic mode is directly depends upon the fourth-order squeezing of the initial pump field. This gives a method of converting higher-order (fourth-order) squeezing into normal squeezing in the harmonic mode and vice versa.

Nonclassical Effects of a Two-Level Spin System Interacting with a Two-Mode Cavity Field via Two-Photon Transition

The interaction of a two-level cyclic XY n-spin model with a two-mode cavity field involving two-photon transitions is investigated through a generalized Jaynes-Cummings model in the rotating-wave approximation. The two-photon interacting Hamiltonian becomes from the replacement of each single-mode field in the one-photon interacting Hamiltonian with the second-harmonic generation. It was assumed that initially the correlated field modes are in disentangled coherent states having the same photon distribution and that the spin system is in an excited state. At any time t > 0, the spin system and the field are in an entangled state, in this case, via a unitary time evolution operator. Thus, the spontaneous decay of a spin level was treated by considering the interaction of the two-level spin system with the modes of the universe in the vacuum state. The different cases of interest, characterized in terms of a detuning parameter for each mode, which emerge from nonvanishing commutation relations, were analytically implemented and numerically discussed for various values of the initial mean photon number and spin-photon coupling constants. Photon distribution, time evolution of the spin population inversion, as well as the statistical properties of the field leading to the possible production of nonclassical states, such as antibunched light, violations of the Cauchy-Schwartz inequality, and second- and fourth-order squeezing, are examined. The case of zero detuning of both modes was treated in terms of a linearization of the expansion of the time evolution operator, while in other three cases, the computations were conducted via second- and third-order Dyson perturbation expansion of the time evolution operator matrix elements for the excited and ground states of the spin system, respectively.

Equivalence of second-order sub-Poissonian statistics and fourth-order squeezing for intense light

We study the simultaneous occurrence of second-order sub-Poissonian photon statistics and fourth-order squeezing for the operator Xθ = X1cosθ+X2sinθ, in the displaced state , where the Hermitian operators X1,2 are defined by X1+i X2 = a, the annihilation operator, D(α) = exp(αa+−α*a) is the displacement operator, α = |α|ei θ and is the state of the weak optical field. We show that the two phenomena occur simultaneously when the amplitude |α| of the displacement is very large as compared to the amplitude of the weak optical field. We also propose a balanced homodyne method for detection of fourth-order squeezed light in the same fashion as that for normal squeezing.

Short-time fourth-order squeezing effects in spontaneous and stimulated four- and six-wave mixing processes

The concept of fourth-order squeezing of the electromagnetic field is investigated in the fundamental mode in spontaneous and stimulated four- and six-wave mixing processes under the short-time approximation based on a fully quantum mechanical approach. The coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators are established. The possibility of obtaining fourth-order squeezing is studied. The dependence of fourth-order squeezing on the number of photons is also investigated. It is shown that fourth-order squeezing, which is a higher-order squeezing, allows a much larger fractional noise reduction than lower-order squeezing. It is shown that squeezing is greater in a stimulated process than the corresponding squeezing in spontaneous interaction. The conditions for obtaining maximum and minimum squeezing are obtained. We have also established the non-classical nature of squeezed radiation using the Glauber–Sudarshan representation.

Generation of higher-order squeezing in a micromaser

The fourth-order squeezing and amplitude-squared squeezing of cotangent states produced in one-atom micromasers are investigated. It is found that optimal squeezing in the cotangent state can be achieved by properly choosing the relative amplitudes of the atomic coherent state. From our study of the dynamic process of the generation of steady-state fourth-order squeezing and amplitude-squared squeezing in one-atom micromasers, it is also shown that for sufficiently large atomic flux, the cavity loss, and finite temperature in the cavity have very little influence on the generation of these higher-order squeezings in practice.

INFLUENCE OF CAVITY LOSS ON GENERATION OF STEADY STATE FOURTH-ORDER AND SQUARED AMPLITUDE SQUEEZING IN MICROMASER

The generation of the steady state fourth-order squeezing and squared amplitude squeezing in a micromaser by the coherent trapping approach is investigated. The results show that if two-level atoms injected into the cavity are initially in coherent state and the flight time of the atoms inside the cavity satisfies the trapping condition, the field can evolve into a coherent trapping state which exhibits steady state fourth-order squeezing and squared amplitude squeezing in the cavity as long as the flux of the atoms is moderately large.

Simultaneous fourth-order squeezing of both quadrature components.

Simultaneous fourth-order squeezing of both quadrature components.

Generation of phase-sensitive nonclassical effects via decay of light into a phase-insensitive environment

We show that phase-sensitive nonclassical effects can be transiently produced via decay of a field mode into a heat bath. In particular, we analyze the time evolution of the fourth-order squeezing of the field mode and we show that under certain conditions the light field which initially was not fourth-order squeezed may exhibit this nonclassical effect. We have found general conditions under which the reduction of higher-order moments of quadrature operators can be observed and eventually the fourth-order squeezing can be produced.

Squeezing Properties of Jaynes-Cummings Fields in Heat Baths

Abstract It is well-known that the field in the Jaynes-Cummings model shows second-order and fourth-order quadrature squeezing. We study the influence of a heat bath reservoir on the squeezing properties of the Jaynes-Cummings field. The experimental realization of the Jaynes-Cummings model is the one-atom maser. Instead of introducing the cavity loss from the first instance of the atom-field interaction we consider the cavity loss only after the atom leaves the cavity under the assumption of strong coupling of the atom with the cavity field as in micromaser theory. In this way we can suggest an optimum span of time to preserve the squeezing properties of the Jaynes-Cummings field. We first investigate the thermal decay of the Fock state and with use of this analytical result we study the evolution of squeezing properties of the cavity field surrounded by the heat bath. Unlike the monotonic decay of second-order squeezing, we find an interesting result of enhancement of fourth-order squeezing during the dissipation process. We extensively analyse the enhancement of fourth-order squeezing through the dissipation process so as to apply the analysis to the case of decay of an arbitrary field state into the vacuum.

Superpositions of coherent states: Squeezing and dissipation.

In this paper we discuss the nonclassical properties of quantum superpositions of coherent states of light. Using general expressions for the Wigner functions of superposition states we analyze the consequences of quantum interference between coherent states. We describe in detail nonclassical properties of a superposition of two coherent states. In particular, we study the oscillatory behavior of the photon number distribution of the even and odd coherent states. We show under which conditions a superposition of two coherent states can exhibit second- and fourth-order squeezing or sub-Poissonian photon statistics. We examine the sensitivity of nonclassical effects such as oscillations in the photon number distribution or second-order squeezing to dissipation. We demonstrate that quantities such as the photon number distribution and interferences in phase space are highly sensitive to even a quite small dissipative coupling, because they depend on all moments of the field observables, and higher moments decay more rapidly than lower moments. Quantities such as quadrature squeezing, on the other hand, are more robust against dissipation because they involve only lower moments. Finally, we find a remarkable effect whereby fourth-order squeezing is generated by damping.

Amplification of higher-order squeezing.

We examine the phase-insensitive amplification of three different kinds of higher-order squeezing. In particular, we consider fourth-order squeezing, intrinsic fourth-order squeezing, and amplitude-squared squeezing. It is found that for any input state both fourth-order squeezing and intrinsic fourth-order squeezing disappear at the output if the intensity gain is greater than 2. Amplitude-squared squeezing, on the other hand, can survive amplification at gains slightly greater than 2. Therefore the photon-cloning limit (intensity gain equals 2) is not a fundamental limit to nonclassical behavior.

Squeezing in Nonlinear Birefringent Medium: An Exactly Soluble Model

Abstract Second- and fourth-order squeezing, produced by the propagation of a coherent light beam through a nonlinear birefringent medium, are investigated. The exact solutions for the presented model are obtained. A detailed numerical analysis of the results is performed and presented graphically.

Fourth-order squeezing in the multiphoton Jaynes-Cummings model.

Hong and Mandel's concept of higher-order squeezing [Phys. Rev. Lett. 54, 323 (1985); Phys. Rev. A 32, 974 (1985)] is applied to the generalized multiphoton Jaynes-Cummings model of a single two-level atom interacting with an initially coherent cavity-field mode. The fourth-order squeezing is examined. The field is shown to be intrinsically squeezed to this order for the photon multiple m\ensuremath{\ge}4.

Finite fourth-order squeezing of both quadrature phase components.

In a previous Comment on recent papers by Hong and Mandel, I was able to show that the ``Jackiw state,'' which is infinitesimally different from the coherent state, displays fourth-order squeezing (as defined by Hong and Mandel's criterion) of both quadrature field components; the magnitude of such squeezing is, however, infinitesimal. In this paper an explicit perturbation calculation is given which results in a state with finite fourth-order squeezing of both quadrature components.