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arXiv:quant-ph/0209077 · Physical Review A

Frequency down-conversion through Bose condensation of light

Patrick Navez

Published Jul 11, 2003• 9 citations
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Abstract

We propose an experimental setup allowing one to convert an input light of wavelengths about $1--2\ensuremath{\mu}\mathrm{m}$ into an output light of a lower frequency. The basic principle of operation relies on the nonlinear optical properties exhibited by a microcavity filled with a photonic bandgap material. The light inside this material behaves like an interacting Bose gas susceptible to reach thermal equilibrium and create a Bose-Einstein condensate. Theoretical estimations show that using a fiber grating, a conversion of $1\ensuremath{\mu}\mathrm{m}$ into $1.5\ensuremath{\mu}\mathrm{m}$ is achieved with an input pulse of about 1 ns, and characterized by a peak power of ${10}^{3}\mathrm{W}.$

DOI
10.1103/physreva.68.013811

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We propose an experimental setup allowing one to convert an input light of wavelengths about 1−−2\ensuremathμm1--2\ensuremath{\mu}\mathrm{m}1−−2\ensuremathμm into an output light of a lower frequency. The basic principle of operation relies on the nonlinear optical properties exhibited by a microcavity filled with a photonic bandgap material. The light inside this material behaves like an interacting Bose gas susceptible to reach thermal equilibrium and create a Bose-Einstein condensate. Theoretical estimations show that using a fiber grating, a conversion of 1\ensuremathμm1\ensuremath{\mu}\mathrm{m}1\ensuremathμm into 1.5\ensuremathμm1.5\ensuremath{\mu}\mathrm{m}1.5\ensuremathμm is achieved with an input pulse of about 1 ns, and characterized by a peak power of 103W.{10}^{3}\mathrm{W}.103W.
Bose-Einstein condensation (BEC) is the transition to a macroscopic occupation of the ground state of a system of bosonic particles. In 1995 the first experimental realization of BEC was achieved by condensing a dilute atomic gas [1,2]. It was long thought only massive particles could undergo BEC. However, in 2010 it was shown that photon BEC was achieved in an optical dye-filled microcavity [3]. In 2015, we became the second group to successfully repeat these experiments.\n\nBEC is a phase transition and thus it occurs at thermal equilibrium. To achieve a thermal photon gas the cavity is filled with a fluorescent dye solution. The dye molecules thermalize the photons by means of repeated absorption-emission cycles. We optically pump the cavity. With the pump we determine the number of photons absorbed by the dye, consequently defining a nonvanishing chemical potential. This ensures a conserved photon number. The photons are trapped by the harmonic potential induced by the concave cavity mirrors. Due to the cutoff energy determined by the cavity length, the trapped photons have a dispersion similar to that of a massive particle in a quantum harmonic oscillator. The cavity length is tuned such that the free spectral range is larger than the bandwidth of the dye. Therefore, only one longitudinal mode fits inside the cavity, making the photon gas effectively two-dimensional. We end up with a thermalized two-dimensional photon gas that has the eigenenergies of a quantum harmonic oscillator. The Bose-Einstein distribution function predicts a critical photon number. Pumping the thermal photon gas beyond this critical number will lead to photon BEC.\n\nWe measure the spectral- and spatial distributions of our two-dimensional photon gas. In both distributions we observe photon BEC. Results show the characteristics of a phase transition: the appearance of a sharp peak on top of the thermal cloud that coincides with a converging chemical potential to zero. Both the spectral- and spatial distribution are in agreement with the theoretical distribution of photons with an effective mass in a quantum harmonic oscillator. Expansion of the condensate has been measured. This could indicate nonlinear optical effects such as thermal lensing or repulsive photon-photon interactions.
A Bose-Einstein condensate can be made of photons. The photons are held at thermodynamic equilibrium in a dye-filled microcavity and pumped with a laser. Thermalisation can be demonstrated and above the threshold a Bose-Einstein condensate will form. A Mach-Zehnder interferometer is built and used to measure the spatial and temporal first-order coherence under various conditions. We build a momentum-resolved spectrometer and use it to obtain views into the phase-space distribution of the photon condensate. We put an upper bound on the value of the interaction strength parameter and find that the microcavity system is ergodic even when not at thermal equilibrium. We build a setup to stabilise the pump laser power with the aim to observe the λ-point of the condensate.
A system of identical bosons can exhibit a state of matter in which the ground state is macroscopically occupied. This special state is called Bose-Einstein condensation, and was predicted by Satyendra Nath Bose and Albert Einstein in 1924. It took some time before physicists achieved this experimentally, but in 1995 it was done by Eric Cornell and Carl Wieman. Since photons are also bosonic particles, they should be able to achieve Bose-Einstein condensation in thermal equilibrium. However this is not as easy for photons as it is for atoms, since the number of photons depends on the temperature. But in 2010 the group of Martin Weitz in Bonn was able to produce a photon Bose-Einstein condensate. This was done using a dye-filled microcavity which is optically pumped. The same principles are used in our setup. Photons inside the cavity thermalize with a fluorescent dye through multiple absorption and emission cycles. The effectively two-dimensional photon gas is trapped by a harmonic potential induced by the shape of the cavity mirrors. This results in photons with eigenenergies of the quantum harmonic oscillator. The minimal energy is determined by the cutoff frequency, set by the cavity length. The thermalization of the photon gas depends on this cutoff frequency, and the total pump power. Jonathan Keeling and Peter Kirton developed a theoretical model describing this system and its thermalization, and simulated it in one dimension.\nWe simulate the same model, in two dimensions using radially averaged photon modes. Threshold for Bose-Einstein condensation is determined for different cutoff frequencies. Our results show good agreement with those of Keeling and Kirton, below, at and above threshold. Multimode condensation and gain clamping of the molecular excitation density are observed above threshold. Comparison with experimental data can only be done qualitatively since it currently is uncalibrated.
Bose–Einstein condensation (BEC) of dressed photons in a Kerr nonlinear optical microcavity is investigated. Our experimental scheme is based on an optical microcavity filled with a Kerr nonlinear nonpolar crystal. The pump photons interact with the Raman phonons in the crystal and hence are converted into new quasiparticles, which we refer to as dressed photons. A dressed photon is a photon dressed with a cloud of virtual transverse-optical phonons. The first main finding is that two-dimensional (2D) dressed photons have an increased inert mass. The second main finding is that the lower cutoff frequency of a nonlinear optical microcavity becomes larger. The third main finding is that the incident laser intensity is a moderate laser intensity ([Formula: see text]10[Formula: see text] W/cm2). The fourth main finding is that the critical optical power of a nonlinear optical microcavity is increased. The fifth main finding is that the radiation emitted by 2D dressed photons has an ultrahigh intensity.
Quantum frequency up-conversion (QFC) of non-classical states of light allows the\nintegration of different quantum systems working at different energies. This process takes\nadvantage of telecommunication wavelengths photons for optical fiber transmission of\nquantum information, and near visible wavelengths for data manipulation and storage.\nThe key objective of QFC is to guarantee that the input photon number probability\ndistribution is maintained after the conversion process. With this, we will be able to\nefficiently study the single-photon emission properties of epitaxial InAs/GaAs quantum\ndots embedded in a photonic crystal nanocavities without the problems that inefficient IR\nwavelengths detectors imply. The up-conversion process consists on combining two\noptical fields, in a nonlinear medium, to generate a third field that is equal to the two inputs\nfrequency sum. To fulfill the momentum conservation, required by this process, we need\nto compensate the wave vector mismatch between the output and input beams. This is\nachieved by using a grating in the nonlinear medium, a process named quasi-phase\nmatching (QPM). In this work we use a Zinc doped periodically poled LiNbO3 (Zn:PPLN\nWG) waveguide as the nonlinear material. To achieve the quantum frequency conversion\nof a semiconductor quantum dot (QD) single photons emission, embedded in a photonic\ncrystal nanocavity, we started by characterizing the performance of the PPLN-WG in the\noptical power macro-regime. Signal photons, produced by an 1175nm laser, simulating\nour QD emission line, are combined with pump photons, produced by a C-band laser,\nwith a dichroic mirror before entering the PPLN waveguide. In order to achieve the phase\nmatched wavelength in the PPLN, its temperature must be finely tuned. The signal\ncoming out of the PPLN waveguide is filtered and analyzed.
Bose-Einstein condensation is a state of matter for which massive bosons develop a macroscopic occupation of the ground state. After the theoretical discovery by Bose and Einstein, it took approximately 70 years to be experimentally realized using Rubidium-87 atoms. Ever since, many different species have been shown to Bose condense. The key in these experiments is cooling down atoms temperatures below 200 nK, while maintaining a large density. Despite all these species, it was thought that photons could not Bose condense. This changed in 2010 when the first Bose-Einstein condensate of photons (phBEC) was achieved. In a table top experiment photons are confined to a dye-filled microcavity where under the right conditions a thermalized photon gas is achieved. Using our setup, we quantitatively show from both the spectral and spatial distribution of photons in the microcavity that a macroscopic occupation of the ground state is achieved, i.e. a condensate of photons. The achievement of phBEC in a dye-filled microcavity has led to a renewed interest in the density distribution of the ideal Bose gas in a two-dimensional harmonic oscillator. We present measurements of the radial profile of photons inside the microcavity below and above the critical point for phBEC with a large signal-to-noise ratio. We obtain good agreement with theoretical profiles obtained using exact summation of eigenstates. An interesting open question is, whether the photons in the condensate are interacting or non-interacting and as a consequence, whether the condensate is also a superfluid or only forms a macroscopically occupied ground state, as predicted by Einstein. When increasing the photon density, we observe an increase in the radius of the condensate which we attribute to effective repulsive interactions. For several dye concentrations we accurately determine the radius of the condensate as a function of the number of condensate photons, and derive from the measurements an effective interaction strength. In many systems ranging from condensed matter physics and particle physics to cosmology, phase transitions and spontaneous symmetry breaking play a crucial role. The information of a polarized condensate from an unpolarized thermal cloud constitutes a directly observable prototype of spontaneous symmetry breaking. For every single-shot of the pump laser, we determine the Stokes parameters of the photons inside the microcavity which fully characterizes the polarization state of the sample. By varying experimental parameters, we investigate if the polarization is randomly chosen from shot-to-shot of the experiment. The dye-filled microcavity is a beautiful tool to achieve phBEC. However, it cannot provide the periodic potential required to achieve quantum phase transitions, such as the Mott insulator that have been so successfully exploited in the field of ultra-cold atoms. We use a local density approach to simulate large-area photonic crystal cavities. Clever interplay with both the electronic and photonic bandgap of these cavities has the potential of achieving phBEC in a periodic potential. We show that when the hole radius varies quadratically as a function of position, the eigenmodes of the photonic crystal can be described by the corresponding eigenmodes of the quantum harmonic oscillator.