Giuseppe Patera

Quantum temporal imaging: application of a time lens to quantum optics

We consider application of a temporal imaging system, based on the sum-frequency generation, to a nonclassical, in particular, squeezed optical temporal waveform. We analyze the restrictions on the pump and the phase matching condition in the summing crystal, necessary for preserving the quantum features of the initial waveform. We show that modification of the notion of the field of view in the quantum case is necessary, and that the quantum field of view is much narrower than the classical one for the same temporal imaging system. These results are important for temporal stretching and compressing of squeezed fields, used in quantum-enhanced metrology and quantum communications.

Quantum coherent control of highly multipartite continuous-variable entangled states by tailoring parametric interactions

AbstractThe generation of continuous-variable multipartite entangled states is important for several protocols of quantum information processing and communication, such as one-way quantum computation or controlled dense coding. In this article we theoretically show that multimode optical parametric oscillators can produce a great variety of such states by an appropriate control of the parametric interaction, what we accomplish by tailoring either the spatio-temporal shape of the pump, or the geometry of the nonlinear medium. Specific examples involving currently available optical parametric oscillators are given, hence showing that our ideas are within reach of present technology.

Temporal imaging with squeezed light

We generalize the scheme of conventional temporal imaging to quantum temporal imaging viable for nonclassical states of light. As an example, we apply our scheme to temporally broadband squeezed light and demonstrate a possibility of its noiseless magnification. In particular, we show that one can magnify by a given factor the coherence time of squeezed light and match it to the response time of the photodetector. This feature opens new possibilities for practical applications of temporally broadband squeezed light in quantum optics and quantum information.

Entanglement of quantum circular states of light

We present a general approach to calculating the entanglement of formation for superpositions of two-mode coherent states, placed equidistantly on a circle in the phase space. We show that in the particular case of rotationally-invariant circular states the Schmidt decomposition of two modes, and therefore the value of their entanglement, are given by analytical expressions. We analyse the dependence of the entanglement on the radius of the circle and number of components in the superposition. We also show that the set of rotationally-invariant circular states creates an orthonormal basis in the state space of the harmonic oscillator, and this basis is advantageous for representation of other circular states of light.

Dissipative structures in optomechanical cavities

Motivated by the increasing interest in the properties of multimode optomechanical devices, here we study a system in which a driven mode of a large-area optical cavity is despersively coupled to a deformable mechanical element. Two different models naturally appear in such scenario, for which we predict the formation of periodic patterns, localized structures (cavity solitons), and domain walls, among other complex nonlinear phenomena. Further, we propose a realistic design based on intracavity membranes where our models can be studied experimentally. Apart from its relevance to the field of nonlinear optics, the results put forward here are a necessary step towards understanding the quantum properties of optomechanical systems in the multimode regime of both the optical and mechanical degrees of freedom.

Noncritical generation of nonclassical frequency combs via spontaneous rotational symmetry breaking

Synchronously pumped optical parametric oscillators (SPOPOs) are optical cavities containing a nonlinear crystal capable of down-converting a frequency comb to lower frequencies. These have received a lot of attention lately, because their intrinsic multimode nature makes them compact sources of quantum correlated light with promising applications in modern quantum information technologies. In this work we show that SPOPOs are also capable of accessing the challenging but interesting regime where spontaneous symmetry breaking plays a crucial role in the quantum properties of the emitted light, difficult to access with any other nonlinear optical cavity. Apart from opening the possibility of studying experimentally this elusive regime of dissipative phase transitions, our predictions will have a practical impact, since we show that spontaneous symmetry breaking provides a specific spatiotemporal mode with perfect squeezing for any value of the system parameters, turning SPOPOs into robust sources of highly nonclassical light above threshold.

Quantum temporal imaging with squeezed light

Temporal imaging is a technique enabling manipulation of temporal optical signals in a manner similar to manipulation of optical images in spatial domain. The quantum description of temporal imaging is relevant in the context of long range quantum communication. Indeed this technology relies on the efficiency of quantum repeaters for which the temporal mode matching between the quantum emitters, the communication network and the quantum memories is critical. In this work we address the problem of temporal imaging of a temporally broadband squeezed light generated by a traveling-wave optical parametric amplifier. We consider a single-lens temporal imaging system formed by two dispersive elements and a parametric temporal lens, based on a non- linear process such as sum-frequency generation or four-wave mixing. We derive a unitary transformation of the field operators performed by this kind of time lens and evaluate the squeezing spectrum at the output of the single-lens imaging system. When the efficiency factor of the temporal lens is smaller than unity, the vacuum fluctuations deteriorate squeezing at its output. For efficiency close to unity, when certain imaging conditions are satisfied, the squeezing spectrum at the output of the imaging system will be the same as that at the output of the OPA in terms of the scaled frequency ΩI = MΩ which corresponds to the scaled time tI = t/M . The magnification factor M gives the possibility of matching the coherence time of the broadband squeezed light to the response time of the photodetector.

Quantum temporal imaging

We study the problem of quantum temporal imaging in the case where the time lens is implemented by a sum frequency generation nonlinear process. We consider the general case where the time lens is characterized by a finite aperture and a not-perfect phase-matching in a regime close to 100% conversion efficiency. In particular we tackle this problem in term of the eigenmodes of the entire transformation of the field in the temporal imaging system. We show that in the case of modeling the phase-matching function by a double Gaussian the eigenmodes are given by chirped Gauss-Hermite functions. The effective number of involved eigenmodes is estimated as the ratio of the temporal aperture of the lens to the walk-off time of the signal and the idler waves in the nonlinear crystal. Our theoretical treatment allows us to identify the criteria for designing imaging schemes with close to unity efficiencies

Temporal imaging with squeezed light (Conference Presentation)

Temporal imaging is a technique that enables manipulation of temporal optical signals in a manner similar to manipulation of optical images in spatial domain. It uses the notion of space-time duality with dispersion phenomena playing the role of diffraction and quadratic phase modulation in time acting as a time lens. In this work we address the problem of temporal imaging of a temporally broadband squeezed light generated by a traveling-wave optical parametric amplifier or a similar device. We consider a single-lens temporal imaging system formed by two dispersive elements and a parametric temporal lens, based on a sum-frequency generation process. We derive a unitary transformation of the field operators performed by this kind of time lens. We evaluate the squeezing spectrum at the output of the single-lens imaging system and find the conditions preserving squeezing in the output field. When the efficiency factor of the temporal lens is smaller than unity, the vacuum fluctuations deteriorate squeezing at its output. For efficiency close to unity, when certain imaging conditions are satisfied, the squeezing spectrum at the output of the imaging system will be the same as that at the output of the OPA. This scheme gives the possibility of matching the coherence time of the broadband squeezed light to the response time of the photodetector. We finally discuss a temporal imaging scheme which allows to partially compensating the frequency dispersion of the OPA.

Quantum coherent control of Gaussian multipartite entanglement

Quantum information has reached a stage where real-world applications stimulate an intense research for the implementation of reliable and practical protocols for quantum communication and information processing. The implementation of such protocols, though, requires distributing quantum correlations (entanglement) among a number of degrees of freedom (modes) increasing with the complexity of the task to achieve. In the large-number-of-modes regime, the most promising example is probably one-way quantum computation in which the computation is achieved by applying local measurements to a set of modes initially in a cluster state [1]. However the generation of multipartite entangled states requires experimental configurations whose complexity increases with the number of the modes involved by means of optical devices. In contrast, a practical source should be compact, scalable, and permit to master the quantum properties of the generated states even when the number of modes is very large. We introduce a general approach for the generation of arbitrary Gaussian multipartite entangled states which is based on the use of naturally multimode parametric down-conversion processes, either in the spatial or in the temporal domain, either for single pass devices or for cavity devices. The advantage of this scheme relies on the fact that the generation of such quantum states can be easily controlled by an experimentally accessible parameter. In general the dynamics of parametric interactions in the low-gain regime is described by a linear operator that couples the different relevant modes.