75 research outputs found
Weakly Interacting Bose Gas in the One-Dimensional Limit
No full textWe prepare a chemically and thermally one-dimensional (1D) quantum degenerate Bose gas in a single microtrap. We introduce a new interferometric method to distinguish the quasicondensate fraction of the gas from the thermal cloud at finite temperature. We reach temperatures down to kT≈0.5ℏω⊥ (transverse oscillator eigenfrequency ω⊥) when collisional thermalization slows down as expected in 1D. At the lowest temperatures the transverse-momentum distribution exhibits a residual dependence on the line density n1D [n subscript 1D], characteristic for 1D systems. For very low densities the approach to the transverse single-particle ground state is linear in n1D [n subscript 1D].European UnionAustrian Science FundDeutsche Forschungsgemeinschaft (DFG)Engineering and Physical Sciences Research Counci
Fluctuations and dissipation in a Bose-Einstein condensed photon gas
No full textBose-Einstein condensation, superfluidity and superconductivity are all related phenomena where particles behave as collective quantum systems. The behavior of such systems is treated using quantum statistics and their properties such as energy distribution or coherence are used to describe the system at a macroscopic level. These quantities are affected not only by the intrinsic features of the particles that constitute the quantum gas, but also by the interaction of these particles with their environment. The effect of a coupling of the quantum gas with its surroundings can be as drastic as completely changing its coherence properties or it might lead to a slight deviation from an equilibrium energy distribution. In this thesis, we investigate the effects caused by coupling a quantum gas of light with its environment.
Quantum gases of light are realized in optical microcavities filled with a medium the photons couple to. If a strong coupling between the light and the medium is realized, the gas comprises mixed states of matter and light such as polaritons. Phenomena like lasing, Bose-Einstein condensation and superfluidity can be observed in such systems. In the opposite case, when the coupling of medium and photons is weak, no coherent coupling is established and the gas consists of pure photons. The latter situation can be experimentally realized in high quality optical microcavities filled with photo-excitable dye molecules. In this system it was shown that if the lifetime of the photons in the cavity are sufficiently long, they thermalize at the temperature of the dye solution. And if the density of the photons is increased beyond a critical point, a Bose-Einstein condensate of photons forms.
A distinct feature of a condensate of photons in the dye-microcavity system compared to atom or polariton condensates is that the dye molecules act as a reservoir of particles, as well as energy. The photon gas exchanges particles with excited dye molecules and the coupling between the two is of statistical nature. It has been shown that Bose-Einstein condensation can coexist with unusually large particle number fluctuations in the so called grand-canonical statistical ensemble regime. In the first part of this thesis, we experimentally investigate the fluctuation-dissipation relation in a Bose-Einstein condensate of photons realized in the dye-microcavity. In equilibrium, thermally driven fluctuations are closely connected to how the system dissipates its excess energy or particles. This relation is so general that it has been observed in a variety of systems ranging from Brownian particles to quantum gases of atoms. However, its validity in Bose-Einstein condensates has not been shown. Despite being intrinsically in thermal equilibrium, fluctuations usually completely diminish in a Bose-Einstein condensate soon after the condensation threshold. We measure the second-order coherence of the photon Bose-Einstein condensate to search for the expected ratio of statistical number fluctuations and compressibility following the fluctuation-dissipation theorem.
Another intriguing aspect of the photon condensate is introduced due to the imperfect reflectivity of the cavity mirrors. In the second part of this thesis we show that this openness can lead to the existence of new states of the condensate. Physical models often consider systems that are completely isolated from their environment, such as a gas of particles closed in a box. Real-life situations often deviate from these idealized scenarios and the system loses energy or particles to its surroundings. In contemporary physics, systems which are dissipatively coupled to the environment are actively studied in a broad range of research fields ranging from optics to biophysics. Here, we investigate the open-system dynamics of a photon condensate in grand-canonical ensemble conditions. We identify non-Hermitian phases of the system that are observed by abrupt changes in the dynamics of the condensate’s second-order coherence
Parametric excitation of the quantum vacuum in nonlinear optical resonators
No full textIn this thesis, I present the generation of correlated photon pairs in high-finesse nonlinear optical micro-resonators. In a first attempt, we utilize the third-order nonlinear material polarization of the dielectric mirror coatings to generate correlated photon pairs via spontaneous four-wave mixing. Two pump photons are annihilated and a pair of signal and idler photons is created, a process where the cavity pump mode couples to adjacent cavity modes. We observe the photon pairs in the first spectral order, i.e. the frequencies are shifted by one free spectral range up- and downwards with respect to the pump mode, driven on the experimentally determined dispersion-compensated cavity resonance. We measure a photon-pair production rate of Γexp = 0.22(1) s-1W-2 with respect to the intra-cavity power. The experiment demonstrates the fast response of the dielectric polarization to the rapidly oscillating standing wave inside the cavity and determines the magnitude of the nonlinearity of the dielectric coating stack.
Even though the size of the nonlinear material is restricted to sub-wavelength scales, i.e. the penetration depth of the electromagnetic wave into the dielectric mirror coating, a measurable amount of photon pairs is generated. In order to increase the stream of photon pairs, we filled a resonator with silicone oil to extend the interaction region to the whole cavity length. We observe a photon-pair production rate of Γexp = (330 ± 30) s-1W-2, which is an increase of more than three orders of magnitude as compared to the empty cavity. The spectral brightness is (44 ± 8) mW-2s-1MHz-1, showing the narrow-band properties of the photon-pair source. Furthermore, we demonstrate the possible tunability of the photon frequencies by changing the spectral separation of the signal and idler mode to the pump mode. This is achieved by using pairs of longitudinal cavity modes shifted by multiples of the free spectral range.
These experiments show a formal equivalence to the dynamical Casimir effect where a time-dependent boundary condition to the electromagnetic field, e.g. an oscillating cavity length, gives rise to the excitation of photon pairs out of the vacuum. Both experiments can thereby be interpreted as the periodic modulation of the refractive index and, hence, the effective cavity length. By changing the pump geometry, we modulate the refractive index in the dielectric mirror coating of a micro-cavity with two dissimilar high-intensity lasers incident from the side of the resonator. The refractive index is then modified at the difference frequency of both lasers, adjusted to be twice the cavity resonance frequency. The modulation couples to the unoccupied cavity mode and gives rise to the creation of correlated photon pairs out of the vacuum state via parametric excitation. The underlying process is distinctive to the former spontaneous four-wave mixing, since one higher frequency pump photon is annihilated and a lower frequency pump photon is generated with the excess creating the photon pair on the unoccupied cavity mode. We measure a correlation signal outstanding almost four standard deviations from the mean accidental coincidence background. We exclude thermal radiation as origin for the observation by reference measurements and estimate the probability of a random appearence of the signal to be less than 0.01 %
Correlations between interacting Rydberg atoms
No full textThis paper is a short introduction to Rydberg physics and quantum nonlinear optics using Rydberg atoms. It has been prepared as a compliment to a series of lectures delivered during the Latin American School of Physics "Marcos Moshinsky" 2017. We provide a short introduction to the properties of individual Rydberg atoms and discuss in detail how the interaction potential between Rydberg atom pairs is calculated. We then discuss how this interaction gives rise to the Rydberg blockade mechanism. With the aid of hallmark experiments in the field applications of the blockade for creating correlated quantum systems are discussed. Our aim is to give an overview of this exciting and rapidly evolving field. The interested reader is referred to original work and more comprehensive reviews and tutorials for further details on these subjects.</p
A memory-based quantum network node with a trapped ion in an optical fibre cavity
No full textExploiting quantum effects in the communication between different systems promise great capabilities as distributed quantum computing or provably secure communication. In this thesis we present the realisation of a memory-based quantum network node as a basic building block for quantum communication. The network node comprises of a single trapped ion as a stationary qubit, which is coupled to a light-matter interface linking the ion to a photonic communication channel. We present the application of an optical resonator, which consists of two opposing mirrors that we have realised at the end of two optical fibres. The small resonator volume (mode volume) increases the light-matter interaction rate, allowing a high bandwidth for the distribution of quantum information in a network via optical photons. In addition, the fibre-based resonator provides intrinsic coupling of the photons to optical fibres, which greatly simplifies their distribution in a network.
We demonstrate the first generation of quantum entanglement between a stationary qubit and a photon, with an optical fibre resonator as the interface between both qubits. Since a quantum state cannot be copied and transmitted classically, entanglement is essential for the purpose of quantum communication. We show that even at a distance (about 1.5 m) the ion and the photon share a common entangled quantum state with a high fidelity of (90.1 ± 1.7)%. The entangled state is generated on-demand by the deterministic excitation of the ion, where we achieve a detection rate of 62 Hz, enabled by the efficient interface between ion and photon.
The presented entanglement between an atom and a photon as two different types of qubits allows us to combine the advantages of information storage (atom) and long range distribution of quantum information (photon). In this context, we demonstrate the first implementation of a provably secure quantum key distribution (QKD) between two remote parties involving an entangled memory qubit. The presented method hereby addresses two principal challenges of quantum key distribution, namely key generation and long-range application. We show that the fundamental quantum mechanical properties of the entangled two-qubit state allow us to generate a key with certifiable randomness, which in this strong form is not possible classically. Furthermore, the presented methods of memory-based key distribution are particularly applicable in the context of quantum repeaters, in which quantum information is temporarily stored before further distribution. This enables long-range key distribution even beyond the point-to-point limit of optical quantum communication, which results from the absorption properties of optical photons as information carriers
Quanten-Rabi Dynamik ultrakalter Atome im Bereich der tiefen starken Kopplung
No full textDas Quanten-Rabi Modell ist eines der einfachsten quantenmechanischen Modelle zur Beschreibung der Wechselwirkung von Licht und Materie als Kopplung einer bosonischen Feldmode und eines Zwei-Niveau-Systems. Während das Jaynes-Cummings Modell als Näherung des Quanten-Rabi Modells für schwache Kopplungen von großer Bedeutung ist, erlauben aktuelle Experimente nun auch größere Kopplungsstärken zu untersuchen, womit das vollständige Quanten-Rabi Modell in den Vordergrund aktueller Untersuchungen rückt. Während Experimente der Resonator-Quantenelektrodynamik den Bereich der ultrastarken Kopplung erreichen, kann der Bereich der tiefen starken Kopplung, bei welcher die charakteristische Energie der Kopplung die restlichen Energien des Systems dominiert, in Quantensimulationen erreicht werden.
In der vorliegenden Arbeit wird die Realisierung einer analogen Quantensimulation des Quanten-Rabi Modells mittels ultrakalter Rubidium-87 Atome in optischen Gitterpotentialen untersucht. Die Quantensimulation basiert auf der Definition eines Zwei-Niveau-Systems auf den untersten beiden Bändern in der Dispersionsrelation eines optischen Mehrphotonengitterpotentials im Blochbild und der Definition einer bosonischen Feldmode in den Bewegungsmoden der Atome in einem harmonischen Dipolfallenpotential. Das harmonische Dipolfallenpotential wird mit dem extrem weit von den atomaren Resonanzen verstimmten Licht eines CO2-Lasers der Wellenlänge 10,6 µm realisiert, was zu langen Kohärenzzeiten führt. Durch Überlagerung des periodischen Gitterpotentials für die Atome mit dem harmonischen Fallenpotential kann ein extrem hoher Wert der Kopplungsstärke zwischen bosonischer Feldmode und dem in den Bloch-Bändern realisierten Zwei-Niveau-System erreicht werden, welcher weit im Bereich der tiefen starken Kopplung des Quanten-Rabi Modells liegt. Dabei wird mehr als der vierfache Wert der relativen Kopplungsstärke bisheriger Realisationen des Modells erreicht, so dass zum ersten Mal in einer analogen Quantensimulation eine deutliche Dominanz der Kopplung über die restlichen Energien beobachtet wird. Es können eine Reihe von theoretisch erwarteten Eigenschaften dieses extremen Parameterbereichs des Quanten-Rabi Modells experimentell untersucht werden, wie der rasche Anstieg der Feldmodenbesetzung bei anfänglicher Präparation des Systems im Vakuumzustand der Feldmode und der Zusammenbruch der in starker und ultrastarker Kopplung auftretenden Vakuum-Rabi-Oszillationen. Die im Experiment beobachtete gute Übereinstimmung der gemessenen Dynamiken der Erwartungswerte mit numerischen Simulationen des Quanten-Rabi Modells bestätigt das Erreichen der tiefen starken Kopplung bei gleichzeitigem Erhalt der Phasenkohärenz des Systems. Die Messungen zeigen, dass mit ultrakalten Atomen in variablen Gitterpotentialen grundlegende Experimente zur Quantenphysik getriebener Systeme in zuvor unerreichten Parameterbereichen realisiert werden können. Perspektiven der Arbeit liegen in der Realisierung neuartiger Phasenübergänge des Spin-Boson Modells sowie in der Quanteninformationsverarbeitung
Detecting Superfluids, Exciting the Higgs Mode and Enhanced Cooling of Dimers in the BEC-BCS Crossover
No full textIn this thesis, the BEC-BCS crossover is experimentally investigated using a quantum simulator apparatus. We prepare a degenerate, interacting fermionic sample by cooling atoms in two of the lowest hyperfine states of 6Li in a crossed optical dipole trap. Interactions between the two states are controlled by means of a broad magnetic Feshbach resonance, and we adjust the samples' temperature and density by preciely tuning the trapping potential. This setup allows us to access and probe the entire BEC-BCS crossover.
A key property of the BEC-BCS crossover is the superfluid critical temperature, predicted to have a maximum on the BEC side of the strongly interacting regime. However, accurately measuring the critical temperature is challenging due to difficulties in determining a reliable temperature scale in the presence of strong interactions. In this thesis, we determine the critical temperature in the crossover with high accuracy by reconstructing the density distribution and incorporating interaction effects in the low-density wings when fitting to the virial expansion of the equation of state. This requires precise identification of the superfluid phase transition onset, for which we have developed two novel advanced image recognition techniques based on machine learning. Our improved methodology confirms, for the first time, an increase in the critical temperature from the BCS limit, extending beyond the unitarity point and approaching the BEC limit.
Crossing the superfluid phase transition is accompanied by spontaneous symmetry breaking, creating an energy landscape that supports two distinct excitation modes: the Goldstone and Higgs modes. Here, we probe the Higgs mode using two distinct excitation methods: a quench and a modulation of the interaction strength. This enables us to observe the Higgs mode throughout the crossover, revealing a gradual fading of the mode as it approaches the BEC regime, where particle-hole symmetry vanishes. Notably, we observe no temperature dependence of the Higgs mode, prompting further research.
Finally, we present a novel cooling method for a strongly interacting Fermi gas on the BEC side of the crossover, where a composite dimer bound state exists. By applying a modulation of the magnetic field at frequencies close to, but higher than the bound state energy, we selectively dissociate and remove high-energy dimers from the trap, thus realising evaporative cooling of the sample. This method does not require any changes to the trapping potential and facilitates staying in the efficient runaway regime. We demonstrate cooling for a wide range of interactions on the BEC side of the crossover, achieving high efficiencies that match or exceed all previously reported forced evaporation cooling near Feshbach resonances
Investigation of Paraxial Light Concentration and Homogeneously Trapped Two-Dimensional Optical Quantum Gases
No full textTrapped degenerate quantum gases in tailored environments allow for the investigation of otherwise unaccessible microscopic phenomena as they appear e.g. for the electron gas inside a solid. The field grew rapidly after the first Bose-Einstein condensate of dilute atomic gases was created in 1995, providing a very illustrative example for the effect of quantum statistics leading to a phase transition when the thermal wavelength of the constituent particles exceeds the mean interparticle distance. Apart from material particles, quantum gases of light can be realized in optical microresonators inside of which the photons interact with a medium. In the regime of strong coupling between photons and the medium, quasi-particles known as polaritons form. Those systems have allowed for the direct investigation of behavior such as superfluidity and superconductivity due to the here established combination of quantum degeneracy and instantaneous contact-like interaction. In our system, the photon gas is created inside a high-finesse optical microcavity that is filled with a liquid dye solution. The thermally related absorption and emission spectra of the dye molecules combined with the strong decoherence due to frequent molecular collisions of dye and solvent molecules allow for the creation of an ensemble that behaves closely to the ideal Bose gas. The short cavity length of several half wave lengths fixes the longitudinal mode number, rendering the gas two-dimensional. Variable potential landscapes for the photon gas can be established via mirror surface topographies, where spherically curved mirrors result in a harmonic oscillator potential for the photon gas and surface-structured plane mirrors can yield finite size box potentials.
In the present work, a quantum degenerate homogeneously trapped two-dimensional photon gas is experimentally realized, providing a novel platform for the investigation of uniform photon gases. Basic properties such as spatial, momentum and spectral distribution are successfully probed and found to be consistent with predictions for the ideal Bose gas at room temperature. Extraction of the specific heat for various photon numbers below and above criticality reveals the absence of a second-order phase transition as expected from theory. Mechanical tilting of one cavity mirror superimposes the trap with a linear potential gradient and allows from the responding density profiles to extract the equation of state and the isothermal compressibility of the gas. The latter is for the ideal Bose gas expected to diverge towards infinity when the system forms into a Bose-Einstein condensate as the macroscopically occupied ground state does not exert any pressure. Owing to the finite size of the sample, this behavior is validated in the quantum degenerate regime but breaks down in the condensed regime due to the nonzero ground state energy.
In other work carried out in this thesis, it is investigated if the apparatus can be employed as a so-called solar light concentrator, as an initially prepared "hot" photon cloud in a harmonic trap is expected to redistribute towards the trap center when cooled to ambient temperature via coupling to the dye heat bath as could potentially be useful for photovoltaic applications. Compared to observed light concentration in dye-doped thin glass-plates that capture a certain fluorescence angle, the here investigated approach relies on systematic reabsorption of trapped fluorescence. Despite observing a shrinking of the cloud, we find that optical losses in the system presently prevent the system from experiencing a phase space density increase
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