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Multimode Effects on a Bose-Einstein Condensate of photons in a Dye-Filled Microcavity

Coenraad Marinissen

Published Jan 1, 2018• 0 citations
OpenAlex

Abstract

In this bachelor’s thesis we study multi-mode effects on the Bose-Einstein condensation (BEC) of photons in a dye-filled microcavity. The repulsive effective interaction of the photons should increase the conden- sate size. We show how the condensate radius of the ground state and an excited state depend on this effective interaction of the photons. We show that the spatial form of the excited state can also decrease the radius of the ground state. For this effect to occur, we expect a sufficiently large effective interaction. Comparing our model with experimental data gives us an effective interaction of g ̃ = (5.2 ± 2.3) × 10−5. However, one should interpret this result with care, because better measurements of the photon occupa- tion numbers are needed before we can reach solid conclusions.\nWe further investigate rate equations for the BEC of photons to understand the stationary photon occupation numbers. We find approximated solutions to these rate equations to find the dependence of the photon occupation numbers on the pump rate which excites the dye molecules in the condensate. Despite those approximations we estimate critical parameters for which either lasing or saturation of the photon numbers is expected. We conclude that the rate of decay from the cavity and emission rates of the dye is very important. From comparing the model with experiment we can conclude that the approximations are well enough to capture the right trend of real data. However, in the limit of large photon numbers, the approximations aren’t good enough anymore and a more accurate approach will be necessary.

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The Effective Interaction Strength in a Bose-Einstein Condensate of Photons in a Dye-Filled Microcavity

S. Greveling, Fons van der Laan, Karindra Perrier +1 more

We experimentally study Bose-Einstein condensation of photons (phBEC) in a dye-filled microcavity. Through multiple absorption and emission cycles the photons inside the microcavity thermalize to the rovibronic temperature of the dye solution. Raising the photon density of the thermalized photon gas beyond the critical photon density yields a macroscopic occupation of the ground state, i.e. phBEC. For increasing density, we observe an increase of the condensate radius 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 an effective interaction strength parameter $\tilde{g}$. For all concentrations we find $\tilde{g} \sim 10^{-2}$, one order larger than previously reported.

arXiv:1712.07922•Dec 21, 2017•0 citations

Photon Bose-Einstein Condensation in a Dye-Filled Microcavity

Karindra Perrier

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.

•May 31, 2016•0 citations

Many-body phenomena in a Bose-Einstein condensate of light

Arie‐Willem de Leeuw

In this thesis we study Bose-Einstein condensation of photons. In Chapter 1 we describe the current experimental set-up and we explain the two important features of the Bose-Einstein condensate of light: dissipation through the interaction with the external reservoir of dye molecules and driving by the external pumping. In Chapter 2 we use the Schwinger-Keldysh formalism to describe the complete time evolution of the light. We show that the finite-lifetime effects of the photons due to the interaction with the dye can be characterized by a single dimensionless parameter, that depends on the power of the external laser pumping the dye. We also determine spectral functions and collective modes of the photon gas in both the normal and the Bose-Einstein condensed phases. In Chapter 3 we demonstrate that the finite-lifetime effects on the spatial first-order correlation functions of the condensed light are negligible, but are important for the temporal first-order correlations. Furthermore, we show that in the normal state the first-order correlations of the photons are suppressed by the interaction with the dye. In Chapter 4 we develop a model to describe the effect of interactions on the number fluctuations in Bose-Einstein condensates. We find good agreement between the observed number fluctuations in the light Bose-Einstein condensate and the results of our model for different interaction strenghts. In Chapter 5 we propose an experiment to observe phase diffusion in the Bose-Einstein condensate of photons and we predict the outcome of individual measurements. In our model we incorporate quantum and thermal fluctuations as well as the finite-lifetime effects. In Chapter 6 we investigate the light in the presence of a periodic potential and we study the transition from a superfluid to a Mott-insulator. We demonstrate that in this system the true Mott-insulating state is longer present due the interactions with the dye molecules. Finally, in Chapter 7 we consider Bose-Einstein condensation of light in nano-fabricated semiconductor microcavities. We demonstrate that in this system there is also a single dimensionless damping parameter that depends on the external pumping. We propose to use the experimental freedom to investigate the superfluidity of the photons via the excitation of scissors modes. We determine the frequency and damping of these scissors modes. We also calculate the density-density correlations of the excited light fluid and we show that this contains a signature of the dynamical Casimir effect.

•Jun 22, 2016•0 citations

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S. Greveling

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.

•Sep 18, 2018•0 citations

Thermalization and Effective Interactions in Photon Condensates

Charly Beulenkamp

The experimental realization of a Bose-Einstein condensate of photons, first achieved in 2010 at Bonn University, allowed for new ways to probe the properties of condensates. For thermal light in free space the chemical potential is zero and condensation is not possible. By confining light to a microcavity, the transverse degrees of freedom behave as massive bosons which can have nonzero chemical potential. The gas of thermal photons can be brought to thermalize with a fluorescent dye though absorption and emission cycles. By pumping the dye molecules with a laser, the chemical potential can be increased and the photons will condense. \nWe have built a setup with which we can spatially and spectrally resolve the photon distribution in such a dye-filled microcavity. This allows us to study the shape and occupation of the low energy transverse modes of the cavity. We use this to investigate the thermalization process of the photon gas. A rate equation model is presented and qualitatively compared to experimental data. We find that the photon gas is not in thermal equilibrium.\nWe also investigate effective photon-photon interactions by measuring the spatial extent of the condensate. We find an effective interaction in the form of thermal lensing. As the thermal lensing depends on the interaction between the photon gas and the dye, we find that the model used for thermalization can also make good predictions about effective photon-photon interactions.

•Jan 1, 2018•0 citations

Interaction and polarization measurements of photon Bose-Einstein condensate

Fons van der Laan

Bose-Einstein condensation (BEC) is a state of matter where bosons macroscopically\noccupy the ground state of a system. In 2010 the group of Martin Weitz achieved a\ntwo-dimensional Bose-Einstein condensation of photons by using a dye-filled micro-\ncavity. In 2015 our research group also achieved a photon BEC using a similar\nsetup. Although one expects the photons to be non-interacting, the radius of the\ncondensate has been shown to grow as a function of photon density. This implies\nrepulse photon-photon interactions. This leads us to question what the strength of\nthe interactions is.\nTo investigate the interaction strength we take single shot images of the photon gas,\nwhile varying the photon density in the cavity. From each image we determine the\nnumber of condensate photons and the radius of the condensate. Subsequently we de-\ntermine the interaction strength to be g = (6.6 +/- 0.7)E-3 and g = (8 +/- 1)E-2\nusing a dye concentration of 1.5 mM and 6.0 mM respectively. This implies that the\ninteraction strength increases for increasing dye concentration. The source of the\ninteractions is not yet understood and should be investigated further.\nWe also determine the polarization state of the photon gas. In order to do so we\nbuild an experimental setup which can measure all four Stokes parameters simulta-\nneously. Since the phase transition into Bose-Einstein condensation is an example of\nspontaneous symmetry breaking, one would expect the condensate to have a differ-\nent polarization each time it is created. We show that this is not the case and that\nevery newly created BEC has the same polarization state, i.e. linearly polarized in\nthe horizontal direction. We show this symmetry breaking is not affected by the dye\nconcentration, photon density inside the cavity or the cavity mirrors. It is however\ncaused by the intra-cavity polarization of the pump beam. We show that we can\nrotate the direction of the polarization by rotating the intra-cavity polarization of\nthe pump beam.

•Jan 1, 2017•0 citations
In this bachelor’s thesis we study multi-mode effects on the Bose-Einstein condensation (BEC) of photons in a dye-filled microcavity. The repulsive effective interaction of the photons should increase the conden- sate size. We show how the condensate radius of the ground state and an excited state depend on this effective interaction of the photons. We show that the spatial form of the excited state can also decrease the radius of the ground state. For this effect to occur, we expect a sufficiently large effective interaction. Comparing our model with experimental data gives us an effective interaction of g ̃ = (5.2 ± 2.3) × 10−5. However, one should interpret this result with care, because better measurements of the photon occupa- tion numbers are needed before we can reach solid conclusions.\nWe further investigate rate equations for the BEC of photons to understand the stationary photon occupation numbers. We find approximated solutions to these rate equations to find the dependence of the photon occupation numbers on the pump rate which excites the dye molecules in the condensate. Despite those approximations we estimate critical parameters for which either lasing or saturation of the photon numbers is expected. We conclude that the rate of decay from the cavity and emission rates of the dye is very important. From comparing the model with experiment we can conclude that the approximations are well enough to capture the right trend of real data. However, in the limit of large photon numbers, the approximations aren’t good enough anymore and a more accurate approach will be necessary.
We experimentally study Bose-Einstein condensation of photons (phBEC) in a dye-filled microcavity. Through multiple absorption and emission cycles the photons inside the microcavity thermalize to the rovibronic temperature of the dye solution. Raising the photon density of the thermalized photon gas beyond the critical photon density yields a macroscopic occupation of the ground state, i.e. phBEC. For increasing density, we observe an increase of the condensate radius 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 an effective interaction strength parameter g~\tilde{g}g~​. For all concentrations we find g~∼10−2\tilde{g} \sim 10^{-2}g~​∼10−2, one order larger than previously reported.
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.
In this thesis we study Bose-Einstein condensation of photons. In Chapter 1 we describe the current experimental set-up and we explain the two important features of the Bose-Einstein condensate of light: dissipation through the interaction with the external reservoir of dye molecules and driving by the external pumping. In Chapter 2 we use the Schwinger-Keldysh formalism to describe the complete time evolution of the light. We show that the finite-lifetime effects of the photons due to the interaction with the dye can be characterized by a single dimensionless parameter, that depends on the power of the external laser pumping the dye. We also determine spectral functions and collective modes of the photon gas in both the normal and the Bose-Einstein condensed phases. In Chapter 3 we demonstrate that the finite-lifetime effects on the spatial first-order correlation functions of the condensed light are negligible, but are important for the temporal first-order correlations. Furthermore, we show that in the normal state the first-order correlations of the photons are suppressed by the interaction with the dye. In Chapter 4 we develop a model to describe the effect of interactions on the number fluctuations in Bose-Einstein condensates. We find good agreement between the observed number fluctuations in the light Bose-Einstein condensate and the results of our model for different interaction strenghts. In Chapter 5 we propose an experiment to observe phase diffusion in the Bose-Einstein condensate of photons and we predict the outcome of individual measurements. In our model we incorporate quantum and thermal fluctuations as well as the finite-lifetime effects. In Chapter 6 we investigate the light in the presence of a periodic potential and we study the transition from a superfluid to a Mott-insulator. We demonstrate that in this system the true Mott-insulating state is longer present due the interactions with the dye molecules. Finally, in Chapter 7 we consider Bose-Einstein condensation of light in nano-fabricated semiconductor microcavities. We demonstrate that in this system there is also a single dimensionless damping parameter that depends on the external pumping. We propose to use the experimental freedom to investigate the superfluidity of the photons via the excitation of scissors modes. We determine the frequency and damping of these scissors modes. We also calculate the density-density correlations of the excited light fluid and we show that this contains a signature of the dynamical Casimir effect.
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.
The experimental realization of a Bose-Einstein condensate of photons, first achieved in 2010 at Bonn University, allowed for new ways to probe the properties of condensates. For thermal light in free space the chemical potential is zero and condensation is not possible. By confining light to a microcavity, the transverse degrees of freedom behave as massive bosons which can have nonzero chemical potential. The gas of thermal photons can be brought to thermalize with a fluorescent dye though absorption and emission cycles. By pumping the dye molecules with a laser, the chemical potential can be increased and the photons will condense. \nWe have built a setup with which we can spatially and spectrally resolve the photon distribution in such a dye-filled microcavity. This allows us to study the shape and occupation of the low energy transverse modes of the cavity. We use this to investigate the thermalization process of the photon gas. A rate equation model is presented and qualitatively compared to experimental data. We find that the photon gas is not in thermal equilibrium.\nWe also investigate effective photon-photon interactions by measuring the spatial extent of the condensate. We find an effective interaction in the form of thermal lensing. As the thermal lensing depends on the interaction between the photon gas and the dye, we find that the model used for thermalization can also make good predictions about effective photon-photon interactions.
Bose-Einstein condensation (BEC) is a state of matter where bosons macroscopically\noccupy the ground state of a system. In 2010 the group of Martin Weitz achieved a\ntwo-dimensional Bose-Einstein condensation of photons by using a dye-filled micro-\ncavity. In 2015 our research group also achieved a photon BEC using a similar\nsetup. Although one expects the photons to be non-interacting, the radius of the\ncondensate has been shown to grow as a function of photon density. This implies\nrepulse photon-photon interactions. This leads us to question what the strength of\nthe interactions is.\nTo investigate the interaction strength we take single shot images of the photon gas,\nwhile varying the photon density in the cavity. From each image we determine the\nnumber of condensate photons and the radius of the condensate. Subsequently we de-\ntermine the interaction strength to be g = (6.6 +/- 0.7)E-3 and g = (8 +/- 1)E-2\nusing a dye concentration of 1.5 mM and 6.0 mM respectively. This implies that the\ninteraction strength increases for increasing dye concentration. The source of the\ninteractions is not yet understood and should be investigated further.\nWe also determine the polarization state of the photon gas. In order to do so we\nbuild an experimental setup which can measure all four Stokes parameters simulta-\nneously. Since the phase transition into Bose-Einstein condensation is an example of\nspontaneous symmetry breaking, one would expect the condensate to have a differ-\nent polarization each time it is created. We show that this is not the case and that\nevery newly created BEC has the same polarization state, i.e. linearly polarized in\nthe horizontal direction. We show this symmetry breaking is not affected by the dye\nconcentration, photon density inside the cavity or the cavity mirrors. It is however\ncaused by the intra-cavity polarization of the pump beam. We show that we can\nrotate the direction of the polarization by rotating the intra-cavity polarization of\nthe pump beam.