Showing papers on "Quantum published in 2004"
TL;DR: A general approach for fabricating inorganically coupled colloidal quantum dots and rods, connected epitaxially at branched and linear junctions within single nanocrystal heterostructures, which allows investigation of potential applications ranging from quantum information processing to artificial photosynthesis.
Abstract: The development of colloidal quantum dots has led to practical applications of quantum confinement, such as in solution-processed solar cells1, lasers2 and as biological labels3. Further scientific and technological advances should be achievable if these colloidal quantum systems could be electronically coupled in a general way. For example, this was the case when it became possible to couple solid-state embedded quantum dots into quantum dot molecules4,5. Similarly, the preparation of nanowires with linear alternating compositions—another form of coupled quantum dots—has led to the rapid development of single-nanowire light-emitting diodes6 and single-electron transistors7. Current strategies to connect colloidal quantum dots use organic coupling agents8,9, which suffer from limited control over coupling parameters and over the geometry and complexity of assemblies. Here we demonstrate a general approach for fabricating inorganically coupled colloidal quantum dots and rods, connected epitaxially at branched and linear junctions within single nanocrystals. We achieve control over branching and composition throughout the growth of nanocrystal heterostructures to independently tune the properties of each component and the nature of their interactions. Distinct dots and rods are coupled through potential barriers of tuneable height and width, and arranged in three-dimensional space at well-defined angles and distances. Such control allows investigation of potential applications ranging from quantum information processing to artificial photosynthesis.
1,149 citations
Journal Article•
TL;DR: This work shows that the spectral distribution and time-dependent decay of light emitted from excitons confined in the quantum dots are controlled by the host photonic crystal, providing a basis for all-solid-state dynamic control of optical quantum systems.
Abstract: Control of spontaneously emitted light lies at the heart of quantum optics. It is essential for diverse applications ranging from miniature lasers and light-emitting diodes, to single-photon sources for quantum information, and to solar energy harvesting. To explore such new quantum optics applications, a suitably tailored dielectric environment is required in which the vacuum fluctuations that control spontaneous emission can be manipulated. Photonic crystals provide such an environment: they strongly modify the vacuum fluctuations, causing the decay of emitted light to be accelerated or slowed down, to reveal unusual statistics, or to be completely inhibited in the ideal case of a photonic bandgap. Here we study spontaneous emission from semiconductor quantum dots embedded in inverse opal photonic crystals. We show that the spectral distribution and time-dependent decay of light emitted from excitons confined in the quantum dots are controlled by the host photonic crystal. Modified emission is observed over large frequency bandwidths of 10%, orders of magnitude larger than reported for resonant optical microcavities. Both inhibited and enhanced decay rates are observed depending on the optical emission frequency, and they are controlled by the crystals’ lattice parameter. Our experimental results provide a basis for all-solid-state dynamic control
of optical quantum systems.
1,019 citations
TL;DR: By coupling a single-electron transistor to a high-quality factor, 19.7-megahertz nanomechanical resonator, position detection approached that set by the Heisenberg uncertainty principle limit as discussed by the authors.
Abstract: By coupling a single-electron transistor to a high–quality factor, 19.7-megahertz nanomechanical resonator, we demonstrate position detection approaching that set by the Heisenberg uncertainty principle limit. At millikelvin temperatures, position resolution a factor of 4.3 above the quantum limit is achieved and demonstrates the near-ideal performance of the single-electron transistor as a linear amplifier. We have observed the resonator's thermal motion at temperatures as low as 56 millikelvin, with quantum occupation factors of N_(TH) = 58. The implications of this experiment reach from the ultimate limits of force microscopy to qubit readout for quantum information devices.
816 citations
TL;DR: This work proposes a scheme for scalable photonic quantum computation based on cavity-assisted interaction between single-photon pulses that is robust to practical noise and experimental imperfections in current cavity-QED setups.
Abstract: We propose a scheme for scalable photonic quantum computation based on cavity-assisted interaction between single-photon pulses. The prototypical quantum controlled phase-flip gate between the single-photon pulses is achieved by successively reflecting them from an optical cavity with a single-trapped atom. Our proposed protocol is shown to be robust to practical noise and experimental imperfections in current cavity-QED setups.
785 citations
TL;DR: An approximate method for calculating Kubo-transformed real-time correlation functions involving position-dependent operators, based on path integral (Parrinello-Rahman) molecular dynamics, which gives the exact quantum mechanical correlation function at time zero, exactly satisfies the quantum mechanical detailed balance condition.
Abstract: We propose an approximate method for calculating Kubo-transformed real-time correlation functions involving position-dependent operators, based on path integral (Parrinello-Rahman) molecular dynamics. The method gives the exact quantum mechanical correlation function at time zero, exactly satisfies the quantum mechanical detailed balance condition, and for correlation functions of the form C(Ax)(t) and C(xB)(t) it gives the exact result for a harmonic potential. It also works reasonably well at short times for more general potentials and correlation functions, as we illustrate with some example calculations. The method provides a consistent improvement over purely classical molecular dynamics that is most apparent in the low-temperature regime.
719 citations
TL;DR: The experimental generation of single-photon–added coherent states and their complete characterization by quantum tomography are reported and allow one to witness the gradual change from the spontaneous to the stimulated regimes of light emission.
Abstract: Single-photon-added coherent states are the result of the most elementary amplification process of classical light fields by a single quantum of excitation. Being intermediate between a single-photon Fock state (fully quantum-mechanical) and a coherent (classical) one, these states offer the opportunity to closely follow the smooth transition between the particle-like and the wavelike behavior of light. We report the experimental generation of single-photon-added coherent states and their complete characterization by quantum tomography. Besides visualizing the evolution of the quantum-to-classical transition, these states allow one to witness the gradual change from the spontaneous to the stimulated regimes of light emission.
656 citations
Posted Content•
TL;DR: This paper focuses on quantum information protocols, which exploit quantum-mechanical effects in an essential way and form the basis for novel and potentially very important applications to secure and fault-tolerant communication and computation.
Abstract: We study quantum information and computation from a novel point of view. Our approach is based on recasting the standard axiomatic presentation of quantum mechanics, due to von Neumann, at a more abstract level, of compact closed categories with biproducts. We show how the essential structures found in key quantum information protocols such as teleportation, logic-gate teleportation, and entanglement-swapping can be captured at this abstract level. Moreover, from the combination of the --apparently purely qualitative-- structures of compact closure and biproducts there emerge `scalars` and a `Born rule'. This abstract and structural point of view opens up new possibilities for describing and reasoning about quantum systems. It also shows the degrees of axiomatic freedom: we can show what requirements are placed on the (semi)ring of scalars C(I,I), where C is the category and I is the tensor unit, in order to perform various protocols such as teleportation. Our formalism captures both the information-flow aspect of the protocols (see quant-ph/0402014), and the branching due to quantum indeterminism. This contrasts with the standard accounts, in which the classical information flows are `outside' the usual quantum-mechanical formalism.
636 citations
01 Jan 2004
TL;DR: An experiment for creating quantum superposition states involving of the order of 10(14) atoms via the interaction of a single photon with a tiny mirror using a combination of state-of-the-art technologies is proposed.
616 citations
CERN1
TL;DR: The boundary effective action of the Dvali-Gabadadze-Porrati model has been studied in this paper, where it is shown that the truncation of this action to the bending mode π consistently describes physics in a wide range of regimes both at the classical and at the quantum level.
Abstract: We study the Dvali-Gabadadze-Porrati model by the method of the boundary effective action. The truncation of this action to the bending mode π consistently describes physics in a wide range of regimes both at the classical and at the quantum level. The Vainshtein effect, which restores agreement with precise tests of general relativity, follows straightforwardly. We give a simple and general proof of stability, i.e. absence of ghosts in the fluctuations, valid for most of the relevant cases, like for instance the spherical source in asymptotically flat space. However we confirm that around certain interesting self-accelerating cosmological solutions there is a ghost. We consider the issue of quantum corrections. Around flat space π becomes strongly coupled below a macroscopic length of 1000 km, thus impairing the predictivity of the model. Indeed the tower of higher dimensional operators which is expected by a generic UV completion of the model limits predictivity at even larger length scales. We outline a non-generic but consistent choice of counterterms for which this disaster does not happen and for which the model remains calculable and successful in all the astrophysical situations of interest. By this choice, the extrinsic curvature Kµ� acts roughly like a dilaton field controlling the strength of the interaction and the cut-off scale at each space-time point. At the surface of Earth the cutoff is ∼ 1 cm but it is unlikely that the associated quantum effects be observable in table top experiments.
575 citations
TL;DR: In this article, the hole mobility of oligoacene crystals was estimated using quantum mechanics and molecular dynamics, and it was shown that an alternative packing into the crystal could lead to 15.2 cm^2/(V s).
Abstract: We estimate the hole mobility for oligoacene crystals using quantum mechanics (QM) to calculate the reorganization energy and electron-transfer coupling matrix elements and molecular dynamics (MD) to do the thermal averaging. Using an incoherent transport model we calculate a hole mobility of 6.5 cm_2/(V s) for pentacene crystals at 300 K. This can be compared to recent experimental results of 5 cm^2/(V s). However, we find that an alternative packing into the crystal could lead to a hole mobility of 15.2 cm^2/(V s). This suggests that current materials might still be improved by a factor of ∼3. Such calculations might be useful for finding solid-state structures that would increase the hole mobility for use in high-performance molecular devices.
550 citations
TL;DR: The numerical prediction, theoretical analysis, and experimental verification of the phenomenon of wave packet revivals in quantum systems has flourished over the last decade and a half as mentioned in this paper, and the theoretical machinery of quantum wave packet construction leading to the existence of revivals and fractional revivals, in systems with one (or more) quantum number(s), as well as how information on the classical period and revival time is encoded in the energy eigenvalue spectrum.
TL;DR: The concept of average logarithmic negativity is introduced, showing that it allows a reliable quantitative estimate of continuo us variable entanglement by direct measurements of global and marginal generalized p-entropies.
Abstract: We investigate the relationship between mixedness and entanglement for Gaussian states of continuous variable systems. We introduce generalized entropies based on Schatten $p$ norms to quantify the mixedness of a state and derive their explicit expressions in terms of symplectic spectra. We compare the hierarchies of mixedness provided by such measures with the one provided by the purity (defined as $\mathrm{tr}\phantom{\rule{0.3em}{0ex}}{\ensuremath{\varrho}}^{2}$ for the state $\ensuremath{\varrho}$) for generic $n$-mode states. We then review the analysis proving the existence of both maximally and minimally entangled states at given global and marginal purities, with the entanglement quantified by the logarithmic negativity. Based on these results, we extend such an analysis to generalized entropies, introducing and fully characterizing maximally and minimally entangled states for given global and local generalized entropies. We compare the different roles played by the purity and by the generalized $p$ entropies in quantifying the entanglement and the mixedness of continuous variable systems. We introduce the concept of average logarithmic negativity, showing that it allows a reliable quantitative estimate of continuous variable entanglement by direct measurements of global and marginal generalized $p$ entropies.
15 Dec 2004
TL;DR: In this paper, functional integral techniques are used to connect the far-from-equilibrium dynamics at early times with the approach to thermal equilibrium at late times, which is crucial for a wide range of phenomena.
Abstract: There has been substantial progress in recent years in the quantitative understanding of the nonequilibrium time evolution of quantum fields. Important topical applications, in particular in high energy particle physics and cosmology, involve dynamics of quantum fields far away from the ground state or thermal equilibrium. In these cases, standard approaches based on small deviations from equilibrium, or on a sufficient homogeneity in time underlying kinetic descriptions, are not applicable. A particular challenge is to connect the far‐from‐equilibrium dynamics at early times with the approach to thermal equilibrium at late times. Understanding the “link” between the early‐ and the late‐time behavior of quantum fields is crucial for a wide range of phenomena. For the first time questions such as the explosive particle production at the end of the inflationary universe, including the subsequent process of thermalization, can be addressed in quantum field theory from first principles. The progress in this field is based on efficient functional integral techniques, so‐called n‐particle irreducible effective actions, for which powerful nonperturbative approximation schemes are available. Here we give an introduction to these techniques and show how they can be applied in practice. Though we focus on particle physics and cosmology applications, we emphasize that these techniques can be equally applied to other nonequilibrium phenomena in complex many body systems.
[...]
01 Oct 2004
TL;DR: In this article, the authors present a proof-of-principle device, a diffusive temperature Brownian motor, which is particularly simple to implement experimentally in order to optimize and selectively control a rich variety of directed transport behaviors.
Abstract: In systems possessing a spatial or dynamical symmetry breaking thermal Brownian motion combined with unbiased, non-equilibrium noise gives rise to a channelling of chance that can be used to exercise control over systems at the micro- and even on the nano-scale. This theme is known as ``Brownian motor'' concept. The constructive role of (the generally overdamped) Brownian motion is exemplified for a noise-induced transport of particles within various set-ups. We first present the working principles and characteristics with a proof-of-principle device, a diffusive temperature Brownian motor. Next, we consider very recent applications based on the phenomenon of signal mixing. The latter is particularly simple to implement experimentally in order to optimize and selectively control a rich variety of directed transport behaviors. The subtleties and also the potential for Brownian motors operating in the quantum regime are outlined and some state-of-the-art applications, together with future roadways, are presented.
CERN1
TL;DR: In this article, the authors study the Dvali-Gabadadze-Porrati model by the method of the boundary effective action and give a simple and general proof of stability, i.e. absence of ghosts in the fluctuations.
Abstract: We study the Dvali-Gabadadze-Porrati model by the method of the boundary effective action. The truncation of this action to the bending mode \pi consistently describes physics in a wide range of regimes both at the classical and at the quantum level. The Vainshtein effect, which restores agreement with precise tests of general relativity, follows straightforwardly. We give a simple and general proof of stability, i.e. absence of ghosts in the fluctuations, valid for most of the relevant cases, like for instance the spherical source in asymptotically flat space. However we confirm that around certain interesting self-accelerating cosmological solutions there is a ghost. We consider the issue of quantum corrections. Around flat space \pi becomes strongly coupled below a macroscopic length of 1000 km, thus impairing the predictivity of the model. Indeed the tower of higher dimensional operators which is expected by a generic UV completion of the model limits predictivity at even larger length scales. We outline a non-generic but consistent choice of counterterms for which this disaster does not happen and for which the model remains calculable and successful in all the astrophysical situations of interest. By this choice, the extrinsic curvature K_{\mu
u} acts roughly like a dilaton field controlling the strength of the interaction and the cut-off scale at each space-time point. At the surface of Earth the cutoff is \sim 1 cm but it is unlikely that the associated quantum effects be observable in table top experiments.
TL;DR: This alternative technique uses existing well-defined quantum efficiencies such as ΦPS II, effectively separates regulated and constitutive thermal dissipation processes, does not require the use of Fo and F′o measurements and gives very similar results to the method proposed by Kramer et al.
Abstract: We propose a simplified alternative method for quantifying the partitioning of excitation energy between photochemistry, fluorescence and thermal dissipation. This alternative technique uses existing well-defined quantum efficiencies such as Phi(PS II), leaving no 'excess' efficiency unaccounted for, effectively separates regulated and constitutive thermal dissipation processes, does not require the use of F(o) and F'(o) measurements and gives very similar results to the method proposed by Kramer et al. [(2004) Photosynth Res 79: 209-218]. We demonstrate the use of the technique using chlorophyll fluorescence measurements in grapevine leaves and observe a high dependence on thermal dissipation processes (up to 75%) at both high light and low temperature.
Posted Content•
TL;DR: An overview of quantum walks is given, with emphasis on their algorithmic applications, which are quantum counterparts of Markov chains.
Abstract: Quantum walks are quantum counterparts of Markov chains. In this article, we give a brief overview of quantum walks, with emphasis on their algorithmic applications.
TL;DR: In this article, the authors discuss several recent developments of generalized Floquet theorems, formalisms, and quasienergy methods, beyond the conventional Floquet theorem, for accurate nonperturbative treatment of a broad range of strong-field atomic and molecular processes and phenomena of current interests.
TL;DR: In this paper, a 3D quantum simulator for the silicon nanowire transistor (SNWT) is presented, where the authors use Buttiker probes to simulate the effects of scattering on both internal device characteristics and terminal currents.
Abstract: The silicon nanowire transistor (SNWT) is a promising device structure for future integrated circuits, and simulations will be important for understanding its device physics and assessing its ultimate performance limits. In this work, we present a three-dimensional quantum mechanical simulation approach to treat various SNWTs within the effective-mass approximation. We begin by assuming ballistic transport, which gives the upper performance limit of the devices. The use of a mode space approach (either coupled or uncoupled) produces high computational efficiency that makes our 3D quantum simulator practical for extensive device simulation and design. Scattering in SNWTs is then treated by a simple model that uses so-called Buttiker probes, which was previously used in metal-oxide-semiconductor field effect transistor (MOSFET) simulations. Using this simple approach, the effects of scattering on both internal device characteristics and terminal currents can be examined, which enables our simulator to be used for the exploration of realistic performance limits of SNWTs.
TL;DR: In this article, the maximum extractable work compatible with quantum mechanics was derived and expressed in terms of the density matrix and the Hamiltonian, which is related to the property of majorization: more major states can provide more work.
Abstract: Thermodynamics teaches that if a system initially off-equilibrium is coupled to work sources, the maximum work that it may yield is governed by its energy and entropy. For finite systems this bound is usually not reachable. The maximum extractable work compatible with quantum mechanics ("ergotropy") is derived and expressed in terms of the density matrix and the Hamiltonian. It is related to the property of majorization: more major states can provide more work. Scenarios of work extraction that contrast the thermodynamic intuition are discussed, e.g. a state with larger entropy than another may produce more work, while correlations may increase or reduce the ergotropy.
TL;DR: In this article, a series of 20 ps ab initio molecular dynamic simulations of water at ambient density and temperatures ranging from 300 to 450k are presented, where Car-Parrinello (CP) and Born-Oppenheimer (BO) molecular dynamics techniques are compared for systems containing 54 and 64 water molecules.
Abstract: A series of 20 ps ab initio molecular dynamic simulations of water at ambient density and temperatures ranging from 300 to 450K are presented. Both Car-Parrinello (CP) and Born-Oppenheimer (BO) molecular dynamics techniques are compared for systems containing 54 and 64 water molecules. At 300K, excellent agreement is found between radial distribution functions (RDFs) obtained with BO and CP dynamics, provided an appropriately small value of the fictitious mass parameter is used in the CP simulation. However, we find that the diffusion coefficients computed from CP dynamics are approximately two times larger than the corresponding BO simulations for T>400K, where statistically meaningful comparisons can be made. Overall, both BO and CP dynamics at 300 K yield overstructured RDFs and slow diffusion as compared to experiment. In order to understand these discrepancies, the effect of proton quantum motion is considered with the use of empirical interaction potentials. We find strong evidence that proton quantum effects may have a larger impact than previously thought on structure and diffusion of the liquid.
TL;DR: Good quantitative agreement is found between the experimental observations and microscopic decoherence theory of matter wave interferometer experiments in which C70 molecules lose their quantum behaviour by thermal emission of radiation.
Abstract: Emergent quantum technologies have led to increasing interest in decoherence—the processes that limit the appearance of quantum effects and turn them into classical phenomena. One important cause of decoherence is the interaction of a quantum system with its environment, which ‘entangles’ the two and distributes the quantum coherence over so many degrees of freedom as to render it unobservable. Decoherence theory1,2,3,4 has been complemented by experiments using matter waves coupled to external photons5,6,7 or molecules8, and by investigations using coherent photon states9, trapped ions10 and electron interferometers11,12. Large molecules are particularly suitable for the investigation of the quantum–classical transition because they can store much energy in numerous internal degrees of freedom; the internal energy can be converted into thermal radiation and thus induce decoherence. Here we report matter wave interferometer experiments in which C70 molecules lose their quantum behaviour by thermal emission of radiation. We find good quantitative agreement between our experimental observations and microscopic decoherence theory. Decoherence by emission of thermal radiation is a general mechanism that should be relevant to all macroscopic bodies.
TL;DR: In this article, the authors unify the quantum Zeno effect (QZE) and the ''bang-bang'' (BB) decoupling method for suppressing decoherence in open quantum systems: in both cases strong coupling to an external system or apparatus induces a dynamical superselection rule that partitions the open system's Hilbert space into quantum subspaces.
Abstract: We unify the quantum Zeno effect (QZE) and the ``bang-bang'' (BB) decoupling method for suppressing decoherence in open quantum systems: in both cases strong coupling to an external system or apparatus induces a dynamical superselection rule that partitions the open system's Hilbert space into quantum Zeno subspaces. Our unification makes use of von Neumann' s ergodic theorem and avoids making any of the symmetry assumptions usually made in discussions of BB. Thus we are able to generalize the BB to arbitrary fast and strong pulse sequences, requiring no symmetry, and to show the existence of two alternatives to a pulsed BB: continuous decoupling and pulsed measurements. Our unified treatment enables us to derive limits on the efficacy of the BB method: we explicitly show that the inverse QZE implies that the BB can in some cases accelerate, rather than inhibit, decoherence.
TL;DR: For quantum critical spin chains without disorder, it is known that the entanglement of a segment of N>>1 spins with the remainder is logarithmic in N with a prefactor fixed by the central charge of the associated conformal field theory as discussed by the authors.
Abstract: For quantum critical spin chains without disorder, it is known that the entanglement of a segment of N>>1 spins with the remainder is logarithmic in N with a prefactor fixed by the central charge of the associated conformal field theory. We show that for a class of strongly random quantum spin chains, the same logarithmic scaling holds for mean entanglement at criticality and defines a critical entropy equivalent to central charge in the pure case. This effective central charge is obtained for Heisenberg, XX, and quantum Ising chains using an analytic real-space renormalization-group approach believed to be asymptotically exact. For these random chains, the effective universal central charge is characteristic of a universality class and is consistent with a c-theorem.
TL;DR: In this paper, the continuity of quantum conditional information S(ρ12|ρ2) with respect to the uniform convergence of states and obtaining a bound which is independent of the dimension of the second party was proved.
Abstract: We prove continuity of quantum conditional information S(ρ12|ρ2) with respect to the uniform convergence of states and obtain a bound which is independent of the dimension of the second party. This can, e.g., be used to prove the continuity of squashed entanglement.
TL;DR: It can be shown that the harmonic approximation not only restores the detailed balance condition like all other correction factors, but that it is the only one that also satisfies the fluctuation-dissipation theorem.
Abstract: Several simple quantum correction factors for classical line shapes, connecting dipole autocorrelation functions to infrared spectra, are compared to exact quantum data in both the frequency and time domain. In addition, the performance of the centroid molecular dynamics approach to line shapes and time-correlation functions is compared to that of these a posteriori correction schemes. The focus is on a tunable model that is able to describe typical hydrogen bonding scenarios covering continuously phenomena from tunneling via low-barrier hydrogen bonds to centered hydrogen bonds with an emphasis on floppy modes and anharmonicities. For these classes of problems, the so-called “harmonic approximation” is found to perform best in most cases, being, however, outperformed by explicit centroid molecular dynamics calculations. In addition, a theoretical analysis of quantum correction factors is carried out within the framework of the fluctuation-dissipation theorem. It can be shown that the harmonic approximation not only restores the detailed balance condition like all other correction factors, but that it is the only one that also satisfies the fluctuation-dissipation theorem. Based on this analysis, it is proposed that quantum corrections of response functions in general should be based on the underlying Kubo-transformed correlation functions.
TL;DR: The statistics of heat exchange between two classical or quantum finite systems initially prepared at different temperatures are shown to obey a fluctuation theorem.
Abstract: The statistics of heat exchange between two classical or quantum finite systems initially prepared at different temperatures are shown to obey a fluctuation theorem.
TL;DR: Two results are motivate and review two results that generalize de Finetti's theorem to the quantum mechanical setting: a definetti theorem for quantum states and a de Fintti theorem forquantum operations.
Abstract: The classical de Finetti theorem provides an operational definition of the concept of an unknown probability in Bayesian probability theory, where probabilities are taken to be degrees of belief instead of objective states of nature. In this paper, we motivate and review two results that generalize de Finetti's theorem to the quantum mechanical setting: Namely a de Finetti theorem for quantum states and a de Finetti theorem for quantum operations. The quantum-state theorem, in a closely analogous fashion to the original de Finetti theorem, deals with exchangeable density-operator assignments and provides an operational definition of the concept of an "unknown quantum state" in quantum-state tomography. Similarly, the quantum-operation theorem gives an operational definition of an "unknown quantum operation" in quantum-process tomography. These results are especially important for a Bayesian interpretation of quantum mechanics, where quantum states and (at least some) quantum operations are taken to be states of belief rather than states of nature.
TL;DR: In this paper, the Ponzano-Regge model was used to properly fix all the symmetries of the 3D quantum gravity model, and the construction of the transition amplitudes in the presence of interacting quantum spinning particles was given.
Abstract: We show how to properly gauge fix all the symmetries of the Ponzano–Regge model for 3D quantum gravity. This amounts to doing explicit finite computations for transition amplitudes. We give the construction of the transition amplitudes in the presence of interacting quantum spinning particles. We introduce a notion of operators whose expectation value gives rise to either gauge fixing, introduction of time, or insertion of particles, according to the choice. We give the link between the spin foam quantization and the Hamiltonian quantization. We finally show the link between the Ponzano–Regge model and the quantization of Chern–Simons theory based on the double quantum group of SU(2).