We re-derive the quantum master equation for the decoherence of a massive Brownian particle due to collisions with the lighter particles from a thermal environment. Our careful treatment avoids the occurrence of squares of Dirac delta functions. It leads to a decoherence rate which is smaller by a factor of 2 pi compared to previous findings. This result, which is in agreement with recent experiments, is confirmed by both a physical analysis of the problem and by a perturbative calculation in the weak coupling limit.
A most simple theoretical argument is given in order to explain the quantitative estimate of the effect of collisional decoherence in matter-wave interferometry. The argument highlights the relevance of quantum and classical features in the description of the phenomenon, showing in particular the connection between the formula used for the experimental fit and the loss term in the classical linear Boltzmann equation.
The quantum state of motion of a large and rotating polar molecule can lose coherence through the collisions with gas atoms. We show how the associated quantum master equation for the center of mass can be expressed in terms of the orientationally averaged differential and total scattering cross sections, for which we provide approximate analytic expressions. The master equation is then utilized to quantify collisional decoherence in a interference experiment with polar molecules.
We employ a continuous dynamical decoupling scheme to suppress the decoherence induced by elastic collisions of cold atoms. Using a continuous echo pulse we achieve a thirty-fold increase in the coherence time of Rb87 atoms trapped in a dipole trap. Coherence times of more than 100ms are demonstrated for an ensemble with an optical depth of 120.
We study the emergence and dynamics of pointer states in the motion of a quantum test particle affected by collisional decoherence. These environmentally distinguished states are shown to be exponentially localized solitonic wave functions which evolve according to the classical equations of motion. We explain their formation using the orthogonal unraveling of the master equation, and we demonstrate that the statistical weights of the arising mixture are given by projections of the initial state onto the pointer basis.
The possibility of consistency between the basic quantum principles of quantum mechanics and wave function collapse is reexamined. A specific interpretation of environment is proposed for this aim and applied to decoherence. When the organization of a measuring apparatus is taken into account, this approach leads also to an interpretation of wave function collapse, which would result in principle from the same interactions with environment as decoherence. This proposal is shown consistent with the non-separable character of quantum mechanics.
We study decoherence of the external degree of freedom of a tracer particle moving in a one dimensional dilute Boltzmann gas. We find that phase averaging is the dominant decoherence effect, rather than information exchange between tracer and gas particles. While a coherent superposition of two wave packets with different mean positions quickly turns into a mixed state, it is demonstrated that such superpositions of different momenta are robust to phase averaging, until the two wave packets acquire a different position due to the different velocity of each wave packet.
We study the loss of spatial coherence in the extended wave function of fullerenes due to collisions with background gases. From the gradual suppression of quantum interference with increasing gas pressure we are able to support quantitatively both the predictions of decoherence theory and our picture of the interaction process. We thus explore the practical limits of matter wave interferometry at finite gas pressures and estimate the required experimental vacuum conditions for interferometry with even larger objects.
We consider the collision model of Ziman {\em et al.} and study the robustness of $N$-qubit Greenberger-Horne-Zeilinger (GHZ), W, and linear cluster states. Our results show that $N$-qubit entanglement of GHZ states would be extremely fragile under collisional decoherence, and that of W states could be more robust than of linear cluster states. We indicate that the collision model of Ziman {\em et al.} could provide a physical mechanism to some known results in this area of investigations. More importantly, we show that it could give a clue as to how $N$-partite distillable entanglement would …
We analyze collisional decoherence of atoms or molecules prepared in a coherent superposition of nondegenerate internal states at ultralow temperatures and placed in an ultracold buffer gas. Our analysis is applicable for an arbitrary bath particle/tracer particle mass ratio. Both elastic and inelastic collisions contribute to decoherence. We obtain an expression relating the observable decoherence rate to pairwise scattering properties, specifically the low-temperature scattering amplitudes. We consider the dependence on the bath particle/tracer particle mass ratio for the case of light bath …
Collisions, even though they do not limit the lifetime of quantum information stored in ground state hyperfine coherences, may severely limit the fidelity for quantum memory when they happen during the write and read process. This imposes restrictions on the implementation of quantum processes in thermal vapor cells and their performance as a quantum memory. We study the effect of these collisions in our experiment.
We study the limitations for entanglement due to collisional decoherence in a Bose-Einstein condensate. Specifically we consider relative number squeezing between photons and atoms coupled out from a homogeneous condensate. We study the decay of excited quasiparticle modes due to collisions, in condensates of atoms with one or two internal degrees of freedom. The time evolution of these modes is determined in the linear response approximation to the deviation from equilibrium. We use Heisenberg-Langevin equations to derive equations of motion for the densities and higher correlation functions …
We present expressions demonstrating that collisional decoherence of ultracold atoms or molecules in a coherent superposition of non-degenerate quantum states is suppressed when both the real and imaginary parts of the scattering lengths for the states in the coherent superposition are equal. We show that the rate of collisional decoherence can be enhanced or suppressed by varying an external magnetic field near a Feshbach resonance. For some resonances, the suppression is very dramatic. We propose a method for measuring the scattering length of ultracold particles in excited quantum states ex…
The decoherence of a two-state tunneling molecule, such as a chiral molecule or ammonia, due to collisions with a buffer gas is analyzed in terms of a succession of quantum states of the molecule satisfying the conditions for a consistent family of histories. With $\hbar ω$ the separation in energy of the levels in the isolated molecule and $γ$ a decoherence rate proportional to the rate of collisions, we find for $γ\gg ω$ (strong decoherence) a consistent family in which the molecule flips randomly back and forth between the left- and right-handed chiral states in a stationary Markov process.…
The eigenstate decoherence hypothesis (EDH) asserts that each individual eigenstate of a large closed system is locally classical-like. We test this hypothesis for a heavy particle interacting with a gas of light particles. This system is paradigmatic for studies of the quantum-to-classical transition: The reduced state of the heavy particle is widely believed to rapidly loose any nonclassical features due to the interaction with the gas. Yet, we find numerical evidence that the EDH is violated: certain eigenstates of this model are manifestly non-classical. Only the weak version of EDH referr…
We show that when the Hornberger--Sipe calculation of collisional decoherence is carried out with the squared delta function a delta of energy instead of a delta of the absolute value of momentum, following a method introduced by Diósi, the corrected formula for the decoherence rate is simply obtained. The results of Hornberger and Sipe and of Diósi are shown to be in agreement. As an independent cross-check, we calculate the mean squared coordinate diffusion of a hard sphere implied by the corrected decoherence master equation, and show that it agrees precisely with the same quantity as calcu…
We examine the emergence of objectivity via quantum Darwinism through the use of a collision model, i.e. where the dynamics is modeled through sequences of unitary interactions between the system and the individual constituents of the environment, termed "ancillas". By exploiting versatility of this framework, we show that one can transition from a "Darwinistic" to an "encoding" environment by simply tuning their interaction. Furthermore we establish that in order for a setting to exhibit quantum Darwinism we require a mutual decoherence to occur between the system and environmental ancillas, …
We study dynamics of quantum open systems, paying special attention to those aspects of their evolution which are relevant to the transition from quantum to classical. We begin with a discussion of the conditional dynamics of simple systems. The resulting models are straightforward but suffice to illustrate basic physical ideas behind quantum measurements and decoherence. To discuss decoherence and environment-induced superselection einselection in a more general setting, we sketch perturbative as well as exact derivations of several master equations valid for various systems. Using these equa…
The problem of reduction (wave packet reduction) is reexamined under two simple conditions: Reduction is a last step completing decoherence. It acts in commonplace circumstances and should be therefore compatible with the mathematical frame of quantum field theory and the standard model. These conditions lead to an essentially unique model for reduction. Consistency with renormalization and time-reversal violation suggest however a primary action in the vicinity of Planck's length. The inclusion of quantum gravity and the uniqueness of space-time point moreover to generalized quantum theory, f…
A general expression is derived for the momentum diffusion constant of a small polarizable particle in blackbody radiation, and is shown to be closely related to the long-wavelength collisional decoherence rate for such a particle in a thermal environment. We show how this diffusion constant appears in the steady-state photon emission rate of two dipoles induced by blackbody radiation. We consider in addition the Einstein--Hopf drag force on a small polarizable particle moving in a blackbody field, and derive its fully relativistic form from the Lorentz transformation of forces.
Complex molecules are intriguing objects at the interface between quantum and classical phenomena. Compared to the electrons, neutrons, or atoms studied in earlier matter-wave experiments, they feature a much more complicated internal structure, but can still behave as quantum objects in their center-of-mass motion. Molecules may involve a large number of vibrational modes and highly excited rotational states, they can emit thermal photons, electrons, or even atoms, and they exhibit large cross sections for collisional interactions with residual background gases. This makes them ideal candidat…
We identify the dominant collisional decoherence mechanism which serves to stabilize and super-select the configuration states of chiral molecules. A high-energy description of this effect is compared to the results of the exact molecular scattering problem, obtained by solving the coupled-channel equations. It allows to predict the experimental conditions for observing the collisional suppression of the tunneling dynamics between the left-handed and the right-handed configuration of D2S2 molecules.
We address the microscopic derivation of a quantum master equation in Lindblad form for the dynamics of a massive test particle with internal degrees of freedom interacting through collisions with a background ideal gas. When either internal or centre of mass degrees of freedom can be treated classically, previously established equations are obtained as special cases. If in an interferometric setup the internal degrees of freedom are not detected at the output, the equation can be recast in the form of a generalized Lindblad structure, which describes non-Markovian effects. The effect of inter…
We point out that the celebrated GRW master-equation is invariant under translations, reflecting the homogeneity of space, thus providing a particular realization of a general class of translation-covariant Markovian master-equations. Such master-equations are typically used for the description of decoherence due to momentum transfers between system and environment. Building on this analogy we show the exact relationship between the GRW master-equation and decoherence master-equations, further providing a collisional decoherence model formally equivalent to the GRW master-equation. This allows…
A logarithmic Schrödinger equation with time-dependent coupling to the non-linearity is presented as a model of collisional decoherence of the wavefunction of a quantum particle in position-space. The particular mathematical form of the logarithmic Schrödinger equation has been shown to follow from conditional wave theory, but the validity of the logarithmic Schrödinger equation has not yet been investigated numerically for general initial conditions. Using an operator-splitting approach, we solve the non-linear equation of motion for the wavefunction numerically and compare it it to the solut…
Including collisional decoherence explicitly, phase sensitivity for estimating effective scattering strength $χ$ of a two-component Bose-Einstein condensate is derived analytically. With a measurement of spin operator $\hat{J}_{x}$, we find that the optimal sensitivity depends on initial coherent spin state. It degrades by a factor of $(2γ)^{1/3}$ below super-Heisenberg limit $\propto 1/N^{3/2}$ for particle number $N$ and the dephasing rate $1<\!<γ<N^{3/4}$. With a $\hat{J}_y$ measurement, our analytical results confirm that the phase $ϕ=χt\sim 0$ can be detected at the limit even in the pres…
Hornberger and Vacchini [Phys. Rev. A82, 036101 (2010); arxiv:0907.3018] claim that the specific collisional momentum decoherence, pointed out in my recent work [Phys. Rev. A80, 064104 (2009); arXiv:0905.3908], is already described by their theory. However, I have performed a calculation whereby I disprove the authors' claim and refute their conclusion that my recent work had no advantage over theirs.
The dynamics of two variants of quantum Fisher information under decoherence are investigated from a geometrical point of view. We first derive the explicit formulas of these two quantities for a single qubit in terms of the Bloch vector. Moreover, we obtain analytical results for them under three different decoherence channels, which are expressed as affine transformation matrices. Using the hierarchy equation method, we numerically study the dynamics of both the two information in a dissipative model and compare the numerical results with the analytical ones obtained by applying the rotating…
We derive a quantum master equation which describes the dynamics of the ensemble-averaged state of homogeneous disorder models at short times, and mediates a transition from coherent superpositions into classical mixtures. While each single realization follows unitary dynamics, this decoherencelike behavior arises as a consequence of the ensemble average. The master equation manifestly reflects the translational invariance of the disorder correlations and allows us to relate the disorder-induced dynamics to a collisional decoherence process, where the disorder correlations determine the spatia…
We show how to describe the diffusion of the quantized angular momentum vector of an arbitrarily shaped rigid rotor as induced by its collisional interaction with an environment. We present the general form of the Lindblad-type master equation and relate it to the orientational decoherence of an asymmetric nanoparticle in the limit of small anisotropies. The corresponding diffusion coefficients are derived for gas particles scattering off large molecules and for ambient photons scattering off dielectric particles, using the elastic scattering amplitudes.
We show that the pointer basis distinguished by collisional decoherence consists of exponentially localized, solitonic wave packets. Based on the orthogonal unraveling of the quantum master equation, we characterize their formation and dynamics, and we demonstrate that the statistical weights arising from an initial superposition state are given by the required projection. Since the spatial width of the pointer states can be obtained by accounting for the gas environment in a microscopically realistic fashion, one may thus calculate the coherence length of a strongly interacting gas.
Gravitationally Induced Quantum Decoherence of Macroscopic Objects
The Hakubi Center for Advanced Research, Kyoto University（京都大学白川中心）；Department of Physics, Kyoto University（京都大学物理系）；Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所引力物理与量子信息中心）
We present an alternative formulation of quantum decoherence theory using conditional wave theory (CWT), which was originally developed in molecular physics (also known as exact factorisation methods). We formulate a CWT of a classic model of collisional decoherence of a free particle with environmental particles treated in a long-wavelength limit. In general, the CWT equation of motion for the particle is non-linear, where the non-linearity enters via the CWT gauge fields. For Gaussian wave packets the analytic solutions of the CWT equations are in exact agreement with those from the density …
We combine the collisional picture for open system dynamics and the control of the rate of decoherence provided by the quantum (anti-)Zeno effect to illustrate the temporal unfolding of the redundant encoding of information into a multipartite environment that is at the basis of Quantum Darwinism, and to control it. The rate at which such encoding occurs can be enhanced or suppressed by tuning the dynamical conditions of system-environment interaction in a suitable and remarkably simple manner. This would help the design of a new generation of quantum experiments addressing the elusive phenome…
The prospect of controlling entanglement in interacting quantum systems offers a myriad of technological and scientific promises, given the progress in experimental studies in systems such as ultracold trapped gases. This control is often challenging because of decoherence, the process by which environmental interactions create spurious entanglements that can destroy the desired entanglement. Considering the collisional decoherence that is relevant for quantum measurements utilizing scattering in one-dimensional trapped gases, here we derive a relationship between particle masses and wave pack…
We employ the theoretical framework of positive operator valued measures, to study Markovian open quantum systems. In particular, we discuss how a quantum system influences its environment. Using the theory of indirect measurements, we then draw conclusions about the information we could hypothetically obtain about the system by observing the environment. Although the environment is not actually observed, we can use these results to describe the change of the quantum system due to its interaction with the environment. We apply this technique to two different problems. In the first part, we stu…
Motivated by the recent efforts to describe the gravitational interaction as a classical channel arising from continuous quantum measurements, we study what types of dynamics can emerge from a collisional model of repeated interactions between a system and a set of ancillae. We show that contingent on the model parameters the resulting dynamics ranges from exact unitarity to arbitrarily fast decoherence (quantum Zeno effect). For a series of measurements the effective dynamics includes feedback-control, which for a composite system yields effective interactions between the subsystems. We quant…
We develop a Monte Carlo wave function algorithm for the quantum linear Boltzmann equation, a Markovian master equation describing the quantum motion of a test particle interacting with the particles of an environmental background gas. The algorithm leads to a numerically efficient stochastic simulation procedure for the most general form of this integro-differential equation, which involves a five-dimensional integral over microscopically defined scattering amplitudes that account for the gas interactions in a non-perturbative fashion. The simulation technique is used to assess various limiti…
We derive a quantum master equation in the context of a polymerized open quantum mechanical system for the scattering of a Brownian particle in an ideal gas environment. The model is formulated in a top-down approach by choosing a Hamiltonian with a coupling between the system and environment that is generally associated with spatial decoherence. We extend the existing work on such models by using a non-standard representation of the canonical commutation relations, inspired by the quantization procedure applied in loop quantum gravity, which yields a model in which position operators are repl…
We introduce jumptime unraveling as a distinct description of open quantum systems. As our starting point, we consider quantum jump trajectories, which emerge, physically, from continuous quantum measurements, or, formally, from the unraveling of Markovian quantum master equations. If the stochastically evolving quantum trajectories are ensemble-averaged at specific times, the resulting quantum states are solutions to the associated quantum master equation. We demonstrate that quantum trajectories can also be ensemble-averaged at specific jump counts. The resulting jumptime-averaged quantum st…
We review the quantum version of the linear Boltzmann equation, which describes in a non-perturbative fashion, by means of scattering theory, how the quantum motion of a single test particle is affected by collisions with an ideal background gas. A heuristic derivation of this Lindblad master equation is presented, based on the requirement of translation-covariance and on the relation to the classical linear Boltzmann equation. After analyzing its general symmetry properties and the associated relaxation dynamics, we discuss a quantum Monte Carlo method for its numerical solution. We then revi…
