Femtosecond Quantum Optics



  • Claude Fabre
  • Nicolas Treps
  • Valentina Parigi


  • Young Sik Ra
  • Syamsundar De
  • Mattia Walschaers


  • Clément Jacquard
  • Francesco Arzani
  • Adrien Dufour
  • Luca La Volpe

Femtosecond Quantum Optics

Ultrafast frequency combs have found tremendous utility as precision instruments in domains ranging from frequency metrology, optical clocks, broadband spectroscopy, and absolute distance measurement. This sensitivity originates from the fact that a comb carries a huge number of co- propagating, coherently-locked frequency modes and ultrafast optics with coherent control techniques became a flourishing field over the last decades. Likewise, exploiting the quantum features of light has enabled remarkable progress for the experimental exploration of fundamental physics and has been central to the establishment of the fields of quantum communication and quantum metrology. The global objective of this research line is to bring together these two vibrant fields with the goal of exploring new capabilities that arise from the interplay of the quantum properties of light at extreme timescales and over extremely broad spectra.

The Femto Lab Team works on 4 main projects :

  •  Quantum Frequency Combs
  • Quantum Information Processing
  • Multimode analysis of laser dynamics
  • Quantum metrology

Research project : Quantum Frequency Combs


Quantum Frequency Combs

Ultrafast pulses are beginning to exhibit an increasingly important role in quantum optics and quantum information science due to their inherently unique temporal and spectral structure. For instance, entanglement amongst multiple modes is necessary for implementation of current quantum information protocols in the continuous-variable regime (e.g., as in one-way quantum computing with cluster states). The traditional means for generation of such multimode states is to sequentially mix together individual continuous-wave laser beams exhibiting the desired quantum properties. While successful for a small number of modes, this scheme is clearly not scable as it necessitates an ever-increasing number of optical elements (i.e., an individual cavity for each mode, beam-splittes to mix the modes, etc.). An alternative approach is to begin with a light source that is intrinsically multimode. Toward this end, femtosecond pulses of light contain upwards of 10^5 individual frequencies in a single beam. The introduction of these pulses into a device capable of coupling several frequency modes through a nonlinear interaction produces an entangled, multimode output. Indeed, recent work has demonstrated the use of a synchronously pumped optical parametric oscillator (SPOPO) to generate multimode nonclassical states of light [Pinel 2012].spip

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The output of these devices consists of several orthogonal supermodes, where each supermode is a linear combination of the individual frequency components comprising the femtosecond pulse [Patera 2010]. Importantly, each supermode exhibits a unique temporal structure, and the nonclassical properties of an individual mode may be fully explored with homodyne detection methodologies. Homodyne detection is a projective technique, and the nonclassical properties of a supermode with a given temporal structure are interrogated by means of a local oscillator with an identical structure. The advent of femtosecond pulse shaping methodologies permit the on-demand creation of shaped ultrafast waveforms. Accordingly, computer-controlled, adaptive pulse-shaping techniques may be employed to fully interrogate the quantum properties of each SPOPO output mode.


Furthermore, the shaping of the SPOPO pump pulse opens the additional possibility of direct Hamiltonian manipulation and control over the SPOPO output entanglement. High-finesse control and manipulation of the multimode entanglement should enable exploration of numerous applications in quantum metrology and measurement-based quantum information processing.

Quantum Information Processing


The output of a syncronously pumped optical parametric oscillator (SPOPO) embeds a multimode non-classical state of light in which different frequencies share quantum correlations, i.e. they are entangled. This is due to the fact that the SPOPO act as an ensemble of independent squeezers on a set of modes with a broad spectral profile. Shifting to a description of the state in terms of frequency bands is then equivalent to a linear optical transformation introducing quantum correlations. Entanglement being a central resource in quantum information theory, this renders the SPOPO a good candidate system for the implementation of quantum information processing tasks. The main advantage comes from the fact that, while it is often difficult to create entanglement over a large number of components, in the case of the SPOPO the entire multimode state is produced in one single step and is contained in one beam, making the resource very compact and scalable. Indeed, experiments conducted by our group already demonstrated the full quantum entanglement of up to ten spectral bands , and hundreds of modes are potentially addressable [1, 2, 3].We tackle the problem of using the SPOPO for information processing both exeprimentally and theoretically.

On the theoretical side, several protocols are under study. As the first example, the opportunity of turning the SPOPO into a measurement based quantum computation (MBQC) [4] device in the continuous-variable (CV) regime [5] has been studied [6]. In MBQC, after the creation of an initial highly entangled state, namely a “cluster state”, the information is processed by local measurements on the modes which compose the state. In particular, any gaussian operation can be implemented with homodyne detections [5].

Most often, the creation of multimode entangled state such as cluster states in a quantum optical setup requires a network of beam-splitters and dephasers, which transform the squeezed input modes in entangled output modes [7]. The configuration of this network varies considerably with the state to be generated, and its complexity grows rapidly with the number of modes, which renders this method poorly scalable. Opposite to this, the SPOPO produces the whole entangled state in one step. The suitable modes should then be measured to process information. To this end, we developed a multi-pixel homodyne detection system. The computation is then completed with a digital post-processing stage of the acquired signals. This allows to obtain a simultaneous measure of e.g. the amplitude quadrature on all the modes in a chosen mode basis. The following is a scheme of the experimental setupmbqc

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It is to be noticed that the transformation which brings from the input modes to the modes can be modeled as a unitary matrix (UT), acting on the vector which regroups the annihilation operators associated to the various squeezed input modes (aSQU). The digital recombination leads to a second transformation, which can be described by an orthogonal matrix O. Finally, two other operations on the modes are possible, which can be modeled independently. First, a possible shaping of the local oscillator would correspond to a matrix DLO multiplying the homodyne detection matrix UT. On the other side, a relative dephasing between the input modes, corresponding to the choice of the quadrature of each mode which is squeezed, is modeled by a diagonal matrix DR acting on the modes aSQU. This is summarized by the following figurespip.php

In summary, this method allows for the realization of unitaries on the (possibly numerous) modes in a more compact and efficient way compared to the beam-splitter network, and can be therefore exploited for the simultaneous creation and measurement of cluster states, yielding a gaussian quantum computation.

MBQC in the CV regime was first formulated in terms of ideal infinitely-squeezed states. Being equivalent to perfectly monochromatic waves in mechanical systems, these carry infinite energy and can only be approximated in realistic implementations with highly but finitely squeezed states. It can be shown that this amounts to introducing computation errors. Our group recently proposed a method to mitigate these errors when asymmetric squeezing is present in the modes used to generate the entangled resource [8]. This method directly applies to the SPOPO setup but may also be used in any other physical scheme for the production of cluster states.

For universal (and any faster than classical) quantum computation, the use of more than quadratic (non-gaussian) nonlinearities is required. It is essential then to introduce non gaussian elements in the experiment. Single-photon operations, as photon counting detectors or single photon addition or subtraction, are among the simplest to achieve practically. The possibility of implementing mode-dependent photon subtraction through sum frequency generation has been demonstrated theoretically [9] and the experimental implementation is currently under way. 
Motivated by this, we are also interested in the characterization of the protocols that may be implemented with such resources. These include sub-universal computations (as e.g. boson sampling) and polynomial approximation of unitary non-gaussian gates.

Boson sampling [10] is a protocol exploiting the bosonic statistics of photons to compute the permanent of a unitary matrix, that can represent a linear optical network, a problem which is believed to be classically hard. The interest in this kind of problems is due to the fact that they represent a demonstration of the “better-than-classical” performances allowed exploiting quantum mechanics and the optical setups required are usually much simpler than those necessary for fully universal quantum computation.

Polynomial approximation of unitary gates recently gained some attention due to the practical difficulties of introducing non-gaussian evolution to the state of a light beam by traditional approaches such as high-order optical nonlinearities and photon-counting. In contrast to that, protocols have been proposed for the polynomial approximation of gates using only on/off photodetection on gaussian states or single photon sources and gaussian measurements [11, 12, 13].

Other possible applications of the SPOPO for quantum information processing include secret-sharing protocols. Secret-sharing consists in sending an encoded message to a group of n players in such a way that at least k players need to collaborate in order to faithfully reconstruct the original message (this schemes are more precisely called (n,k) threshold schemes). Classical protocols exist to do this, but quantum correlations can also be exploited to enhance the quality of the retrieved message [14].
Theoretical and experimental studies are currently underway in our lab on this subject in collaboration with the Quantum Information team at Télécom Paris Tech and the Theory group at the Laboratoire MPQ of the University of Paris 7.

[1] Roslund, J., De Araujo, R. M., Jiang, S., Fabre, C., & Treps, N. (2014). Wavelength-multiplexed quantum networks with ultrafast frequency combs. Nature Photonics, 8(2), 109-112.[2] R. Medeiros de Araújo, J. Roslund, Y. Cai, G. Ferrini, C. Fabre, and N. Treps. Full characterization of a highly multimode entangled state embedded in an optical frequency comb using pulse shaping. Phys. Rev. A 89, 053828 (arXiv:1401.4867)[3] S. Gerke, J. Sperling, W. Vogel, Y. Cai, J. Roslund, N. Treps, and C. Fabre. Full multipartite entanglement of frequency comb Gaussian states. Phys. Rev. Lett. 114, 050501 ( arXiv:1409.5692)[4] J. Briegel and R. Raussendorf, Phys. Rev. Lett. 86, 910 (2001) ; R. Raussendorf and H.J. Briegel, Phys. Rev. Lett. 86, 5188 (2001).[5] M. Gu et al, Phys. Rev. A 79, 062318 (2009).[6] Giulia Ferrini, Jean-Pierre Gazeau, Thomas Coudreau, Claude Fabre, Nicolas Treps. Compact Gaussian quantum computation by multi-pixel homodyne detection
. 2013 New J. Phys. 15 093015 (arXiv:1303.5355)[7] R. Ukai et al, Phys. Rev. Lett. 106, 240504 (2011).[8] G. Ferrini, J. Roslund, F. Arzani, Y. Cai, C. Fabre, and N. Treps. Optimization of networks for measurement-based quantum computation. Accepted for publication on Phys. Rev. A.[9] Valentin A. Averchenko, Valérian Thiel, and Nicolas Treps. Non-linear photon subtraction from a multimode quantum field. Phys. Rev. A 89, 063808 (arXiv:1404.0160)[10] Aaronson, S., & Arkhipov, A. (2011, June). In Proceedings of the forty-third annual ACM symposium on Theory of computing (pp. 333-342). ACM.[11] Petr Marek, Radim Filip, and Akira Furusawa. Phys. Rev. A 84, 053802[12] Kimin Park, Petr Marek, and Radim Filip. Phys. Rev. A 90, 013804[13] Kevin Marshall, Raphael Pooser, George Siopsis, Christian Weedbrook, arXiv:1412.0336[14] Andrew M Lance et al 2003 New J. Phys. 5 4

Multimode Analysis of Laser Dynamics



Ultrafast frequency combs (FC) have found tremendous utility as precision instruments in various domains ranging from metrology, spectroscopy, and timekeeping. The noise dynamics of FC are typically described with a succinct number of collective properties, such as the pulse energy, carrier envelope offset, or the temporal jitter of the pulse train. A variation in one of these parameters perturbs the FC in a manner that consists of adding a particular noise mode to the coherent field structure. Thus, the entirety of the FC noise dynamics is described by a set of noise modes in which each mode possesses a particular pulse shape. The existence of such modes would imply a non-negligible role of spectral noise correlations among the individual FC teeth. We are studying spectral correlations of the amplitude and phase noise in a FC.


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In our recent study, we investigated the noise dynamics of FC by utilizing ultrafast pulse shaping combined with quantum noise-limited balanced homodyne detection [Schmeissner 2014]. The above figures show spectral correlations of the amplitude and phase noise in a titanium-sapphire FC. For high sideband frequencies (≥ 2 MHz), the noise in each spectral band is identical and equal to the shot noise limit without any correlations among different spectral bands: figures (a) and (c) show the phase and amplitude noise, respectively. However, correlations among various frequencies are apparent for longer analysis timescales (measured at 500 kHz frequency), as shown in figure (b) for phase noise and figure (d) for amplitude noise. The techniques employed will also find applications in studying noise dynamics of a variety of systems, including both fiber- and microresonator-based FCs for which the noise dynamics are not as thoroughly understood.


Quantum Metrology


Metrology is the science of measuring, and any measurement is a comparison to a given scale. Precise measurements require long term stable reference standards to permit to measure a mean value out any kind of disturbing noise. Light can be such a reference scale, as its properties allow reaching very high precision and sensitivity levels.

Regardless to its generation, the precise properties of light are limited by noise effects emerging from the quantization of light. Any optical measurement is therefore limited by these unavoidable fluctuations, namely the shot noise – or quantum limit. It is important to know what the ultimate sensitivity that can be possibly achieved in a measurement using a light beam is, and how this sensitivity could be enhanced by using quantum resources.

For many years, our group has been studying these limits both theoretically and experimentally. We have in particular recently studied the general theoretical bounds on the estimation of an arbitrary parameter encode in a light beam, and how this parameter can be optimally retrieved in a detection system [Pinel 2012].

The first implementations of these optimal measurement schemes have been carried out in the spatial domain : we have studied the quantum limits in image processing [Fade 2008, Delaubert 2008] and demonstrated experimentally optimal measurements of beam displacement and beam tilt [Delaubert 2006].

The theoretical and experimental study of these limits is the issue of the project FRECQUAM supported by the ERC, combining optical frequency combs as a metrological tool with the framework of quantum optics. It unites in some sense the two parts of the 2005 Nobel Price for optical frequency combs and quantum optics.


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Optical frequency combs consist of a large number of individual optical frequency components with a fixed phase relation over a long coherence time. Being a frequency ruler they are equivalent to a regular train of femtosecond light pulses. The extraordinary stability of their properties permitted measurements with unprecedented precision and makes them perfect tools for high precision metrological applications.

We have studied the theoretical limits of sensitivity in the estimation of parameters encoded in an optical frequency comb, for example a time delay or a dispersion parameter. This lead to the proposal of metrological experiments at the quantum limit, like space-time positioning [Lamine 2008] or dispersion measurement in air [Jian 2012].

In order to experimentally reach the quantum limits in these experiments, we develop and investigate the noise properties of several optical devices : quantum projective measurements, namely the balanced homodyne detection, are used as high sensitivity detection schemes ; passive filtering cavities play an important role in removing classical noise from the frequency combs ; pulse shaping techniques are needed to access the information carried in various temporal modes in balanced homodyne detection.

Further investigations try to generalize the underlying theoretical concept and concern the possible definition of observables on frequency combs parameters.