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arXiv:1409.5388 · Physical Review A

Heating of trapped ultracold atoms by collapse dynamics

Franck Laloë, William J. Mullin, Philip Pearle

Published Nov 24, 2014• 95 citations
arXivHTMLPDF

Abstract

The continuous spontaneous localization (CSL) theory alters the Schr\"odinger equation. It describes wave-function collapse as a dynamical process instead of an ill-defined postulate, thereby providing macroscopic uniqueness and solving the so-called measurement problem of standard quantum theory. CSL contains a parameter $\ensuremath{\lambda}$ giving the collapse rate of an isolated nucleon in a superposition of two spatially separated states and, more generally, characterizing the collapse time for any physical situation. CSL is experimentally testable, since it predicts some behavior different from that predicted by standard quantum theory. One example is the narrowing of wave functions, which results in energy imparted to particles. Here we consider energy given to trapped ultracold atoms. Since these are the coldest samples under experimental investigation, it is worth inquiring how they are affected by the CSL heating mechanism. We examine the CSL heating of a Bose-Einstein condensate (BEC) in contact with its thermal cloud. Of course, other mechanisms also provide heat and also particle loss. From varied data on optically trapped cesium BECs, we present an energy audit for known heating and loss mechanisms. The result provides an upper limit on CSL heating and thereby an upper limit on the parameter $\ensuremath{\lambda}$. We obtain $\ensuremath{\lambda}\ensuremath{\lesssim}1(\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ ${\mathrm{s}}^{\ensuremath{-}1}$.

DOI
10.1103/physreva.90.052119

Related papers

Effects of dynamical collapse theory on trapped ultra-cold atoms

Franck Laloë, William J. Mullin, Philip Pearle

{The Continuous Spontaneous Localization (CSL) theory alters the Schrodinger equation. It describes wave function collapse as a dynamical process instead of an ill-defined postulate, thereby providing macroscopic uniqueness and solving the so-called measurement problem of standard quantum theory. CSL contains a parameter $\lambda$ giving the collapse rate of an isolated nucleon in a superposition of two spatially separated states and, more generally, characterizing the collapse time for any physical situation. CSL is experimentally testable, since it predicts some behavior different from that predicted by standard quantum theory. One example is the narrowing of wave functions, which results in energy imparted to particles. Here we consider energy given to trapped ultra-cold atoms. Since these are the coldest samples under experimental investigation, it is worth inquiring how they are affected by the CSL heating mechanism. We examine the CSL heating of a BEC in contact with its thermal cloud. Of course, other mechanisms also provide heat and also particle loss. From varied data on optically trapped cesium BEC's, we present an energy audit for known heating and loss mechanisms. The result provides an upper limit on CSL heating and thereby an upper limit on the parameter $\lambda$. We obtain $\lambda\lesssim 1(\pm1)\times 10^{-7}$sec$^{-1}$.}

•Sep 18, 2014•0 citations

Collapse in ultracold Bose Josephson junctions

Marco Bilardello, Andrea Trombettoni, Angelo Bassi

We investigate how ultracold atoms in double-well potentials can be used to study and put bounds on models describing wave-function collapse. We refer in particular to the continuous spontaneous localization (CSL) model, which is the most well studied among dynamical reduction models. It modifies the Schr\"odinger equation in order to include the collapse of the wave function in its dynamics. We consider Bose Josephson junctions, where ultracold bosons are trapped in a double-well potential, since they can be experimentally controlled with high accuracy and are suited and used to study macroscopic quantum phenomena on a scale of microns, with a number of particles typically ranging from $\ensuremath{\sim}{10}^{2}--{10}^{3}$ to $\ensuremath{\sim}{10}^{5}--{10}^{6}$. We study the CSL dynamics of three atomic states showing macroscopic quantum coherence: the atomic coherent state, the superposition of two atomic coherent states, and the NOON state. We show that for the last two states, the suppression of quantum coherence induced by the CSL model increases exponentially with the number of atoms. We observe that in the case of optically trapped atoms, the spontaneous photon emission of the atoms induces a dynamics similar to the CSL one, and we conclude that magnetically trapped atoms may be more convenient to experimentally test the CSL model. Finally, we discuss decoherence effects in order to provide reasonable estimates on the bounds that it is (or will be) possible to obtain for the parameters of the CSL model in such class of experiments. As an example, we show that a NOON state with $N\ensuremath{\sim}{10}^{3}$ with a coherence time of $\ensuremath{\sim}1$ s can constrain the CSL parameters in a region where the other systems presently cannot.

arXiv:1612.07691•Physical Review A•Mar 29, 2017•14 citations

Testing wave-function-collapse models using parametric heating of a trapped nanosphere

Daniel Goldwater, Mauro Paternostro, P. F. Barker

We propose a mechanism for testing the theory of collapse models such as continuous spontaneous localization (CSL) by examining the parametric heating rate of a trapped nanosphere. The random localizations of the center of mass for a given particle predicted by the CSL model can be understood as a stochastic force embodying a source of heating for the nanosphere. We show that by utilizing a Paul trap to levitate the particle and optical cooling, it is possible to reduce environmental decoherence to such a level that CSL dominates the dynamics and contributes the main source of heating. We show that this approach allows measurements to be made on the time scale of seconds and that the free parameter ${\ensuremath{\lambda}}_{\mathrm{csl}}$ which characterizes the model ought to be testable to values as low as ${10}^{\ensuremath{-}12}$ Hz.

arXiv:1506.08782•Physical Review A•Jul 14, 2016•96 citations

Detecting continuous spontaneous localization with charged bodies in a Paul trap

Ying Li, Andrew M. Steane, Daniel Bedingham +1 more

Continuous spontaneous localization (CSL) is a model that captures the effects of a class of extensions to quantum theory which are expected to result from quantum gravity and is such that wave-function collapse is a physical process. The rate of such a process could be very much lower than the upper bounds set by searches to date and yet still modify greatly the interpretation of quantum mechanics and solve the quantum measurement problem. Consequently experiments are sought to explore this. We describe an experiment that has the potential to extend sensitivity to CSL by many orders of magnitude. The method is to detect heating of the motion of charged macroscopic objects confined in a Paul trap. We discuss the detection and the chief noise sources. We find that CSL with standard parameters could be observed using a vibration-isolated ion trap of size 1 cm at ultralow pressure with optical interferometric detection.

arXiv:1605.01881•Physical Review A•Mar 13, 2017•39 citations

Heating effects and localization mechanism in cold Bose gases

Marco Bilardello

Collapse models solve the measurement problem by adding non-linear and stochastic terms to the usual Schroedinger dynamics. The resulting dynamics localizes in position macroscopic systems, while preserves quantum mechanical predictions for microscopic systems. \nTwo of the main consequences of this resulting dynamics are: the loss of any initial spatial coherence, with a decoherence rate which increases with the dimensions of the system (amplification mechanism); and a heating effect induced on the system that, for long times, leads either to a divergent or to a convergent value of the energy, depending on the particular collapse model considered. \nAn interesting class of system to experimentally test collapse models are cold atomic gases. Besides their very low temperatures (T = 10^(-11) - 10^(-7)K), cold atomic gases show mesoscopic quantum properties, i.e. involving a number of atoms of order of N = 10^(3)– 10^(11). These are all necessary ingredients to experimentally test collapse models. In this thesis, we use cold bosonic atomic gas to test one of the most studied and complete among collapse models, i.e. CSL, and also its non-Markovian and dissipative extensions. In particular, in this thesis we put bounds on CSL free-parameters by studying the diffusion effect induced by collapse noise on a free expanding gas, and we compare the theoretical results with experimental data known in literature. The bounds we put are among the strongest ever found non only for CSL model, but especially for its non-Markovian extension. \nIn this thesis we also specialize the CSL dynamics in Bose-Josephson junctions, and we focus on the localization mechanism induced by the noise on initially entangled states. In particular, we focus on decoherence induced by CSL on typical entangled states as atomic coherent states and NOON states. We find that in the latter ones, CSL effects become significant when the NOON state is composed by a number of atoms of 10^(4) or greater. Moreover, we compare CSL decoherence with environmental decoherence induced by typical realistic sources, as an external thermal cloud, imperfections in the trapping laser, and three body effects. We then find which conditions experiments must fulfill in order to test CSL in a Bose-Josephson junction in conditions never

•Apr 12, 2017•2 citations

Introduction to Dynamical Wave Function Collapse

Philip Pearle

Abstract This book describes one approach to resolving the ‘measurement problem’ of standard quantum theory (SQT), by changing the Schrodinger equation’s evolution of the wave function. The wave function of SQT does not describe reality. For example, the wave function corresponding to a completed experiment is the sum of terms describing the different experimental outcomes whereas one of these outcomes is what appears in Nature, The rules of SQT respond to this deficiency by imposing an ill-defined ‘collapse postulate.’ The prior smooth evolution of the wave function according to Schrodinger’s equation is replaced by an abrupt ‘jump’ to one of the outcomes. When, why, how are unanswered questions. I have added a term to Schrodinger’s equation, obtaining a theory (which I named the ‘Continuous Spontaneous Localization’ theory, or CSL) that answers these questions. The term has a random field in it: each field makes the sum of terms evolve to one of the terms. The collection of all possible fields produces the (Born rule) probabilistic predictions of SQT. Thus, CSL does something SQT does not: it describes the occurrence of events. But, it is a different theory than SQT, so it predicts different results for some carefully crafted experiments. CSL has now existed for over three decades. While no experiment as yet has proven CSL true, no experiment has conflicted with it either. In this book I have aimed to give a clear exposition of CSL and its consequences, accessible to anyone who has studied SQT.

•Jan 30, 2024•1 citation
The continuous spontaneous localization (CSL) theory alters the Schr"odinger equation. It describes wave-function collapse as a dynamical process instead of an ill-defined postulate, thereby providing macroscopic uniqueness and solving the so-called measurement problem of standard quantum theory. CSL contains a parameter \ensuremathλ\ensuremath{\lambda}\ensuremathλ giving the collapse rate of an isolated nucleon in a superposition of two spatially separated states and, more generally, characterizing the collapse time for any physical situation. CSL is experimentally testable, since it predicts some behavior different from that predicted by standard quantum theory. One example is the narrowing of wave functions, which results in energy imparted to particles. Here we consider energy given to trapped ultracold atoms. Since these are the coldest samples under experimental investigation, it is worth inquiring how they are affected by the CSL heating mechanism. We examine the CSL heating of a Bose-Einstein condensate (BEC) in contact with its thermal cloud. Of course, other mechanisms also provide heat and also particle loss. From varied data on optically trapped cesium BECs, we present an energy audit for known heating and loss mechanisms. The result provides an upper limit on CSL heating and thereby an upper limit on the parameter \ensuremathλ\ensuremath{\lambda}\ensuremathλ. We obtain \ensuremathλ\ensuremath≲1(\ifmmode±\else\textpm\fi1)\ifmmode×\else\texttimes\fi10\ensuremath−7\ensuremath{\lambda}\ensuremath{\lesssim}1(\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}\ensuremathλ\ensuremath≲1(\ifmmode±\else\textpm\fi1)\ifmmode×\else\texttimes\fi10\ensuremath−7 s\ensuremath−1{\mathrm{s}}^{\ensuremath{-}1}s\ensuremath−1.
{The Continuous Spontaneous Localization (CSL) theory alters the Schrodinger equation. It describes wave function collapse as a dynamical process instead of an ill-defined postulate, thereby providing macroscopic uniqueness and solving the so-called measurement problem of standard quantum theory. CSL contains a parameter λ\lambdaλ giving the collapse rate of an isolated nucleon in a superposition of two spatially separated states and, more generally, characterizing the collapse time for any physical situation. CSL is experimentally testable, since it predicts some behavior different from that predicted by standard quantum theory. One example is the narrowing of wave functions, which results in energy imparted to particles. Here we consider energy given to trapped ultra-cold atoms. Since these are the coldest samples under experimental investigation, it is worth inquiring how they are affected by the CSL heating mechanism. We examine the CSL heating of a BEC in contact with its thermal cloud. Of course, other mechanisms also provide heat and also particle loss. From varied data on optically trapped cesium BEC's, we present an energy audit for known heating and loss mechanisms. The result provides an upper limit on CSL heating and thereby an upper limit on the parameter λ\lambdaλ. We obtain λ≲1(±1)×10−7\lambda\lesssim 1(\pm1)\times 10^{-7}λ≲1(±1)×10−7sec−1^{-1}−1.}
We investigate how ultracold atoms in double-well potentials can be used to study and put bounds on models describing wave-function collapse. We refer in particular to the continuous spontaneous localization (CSL) model, which is the most well studied among dynamical reduction models. It modifies the Schr\"odinger equation in order to include the collapse of the wave function in its dynamics. We consider Bose Josephson junctions, where ultracold bosons are trapped in a double-well potential, since they can be experimentally controlled with high accuracy and are suited and used to study macroscopic quantum phenomena on a scale of microns, with a number of particles typically ranging from $\ensuremath{\sim}{10}^{2}--{10}^{3}$ to $\ensuremath{\sim}{10}^{5}--{10}^{6}$. We study the CSL dynamics of three atomic states showing macroscopic quantum coherence: the atomic coherent state, the superposition of two atomic coherent states, and the NOON state. We show that for the last two states, the suppression of quantum coherence induced by the CSL model increases exponentially with the number of atoms. We observe that in the case of optically trapped atoms, the spontaneous photon emission of the atoms induces a dynamics similar to the CSL one, and we conclude that magnetically trapped atoms may be more convenient to experimentally test the CSL model. Finally, we discuss decoherence effects in order to provide reasonable estimates on the bounds that it is (or will be) possible to obtain for the parameters of the CSL model in such class of experiments. As an example, we show that a NOON state with $N\ensuremath{\sim}{10}^{3}$ with a coherence time of $\ensuremath{\sim}1$ s can constrain the CSL parameters in a region where the other systems presently cannot.
We propose a mechanism for testing the theory of collapse models such as continuous spontaneous localization (CSL) by examining the parametric heating rate of a trapped nanosphere. The random localizations of the center of mass for a given particle predicted by the CSL model can be understood as a stochastic force embodying a source of heating for the nanosphere. We show that by utilizing a Paul trap to levitate the particle and optical cooling, it is possible to reduce environmental decoherence to such a level that CSL dominates the dynamics and contributes the main source of heating. We show that this approach allows measurements to be made on the time scale of seconds and that the free parameter ${\ensuremath{\lambda}}_{\mathrm{csl}}$ which characterizes the model ought to be testable to values as low as ${10}^{\ensuremath{-}12}$ Hz.
Continuous spontaneous localization (CSL) is a model that captures the effects of a class of extensions to quantum theory which are expected to result from quantum gravity and is such that wave-function collapse is a physical process. The rate of such a process could be very much lower than the upper bounds set by searches to date and yet still modify greatly the interpretation of quantum mechanics and solve the quantum measurement problem. Consequently experiments are sought to explore this. We describe an experiment that has the potential to extend sensitivity to CSL by many orders of magnitude. The method is to detect heating of the motion of charged macroscopic objects confined in a Paul trap. We discuss the detection and the chief noise sources. We find that CSL with standard parameters could be observed using a vibration-isolated ion trap of size 1 cm at ultralow pressure with optical interferometric detection.
Collapse models solve the measurement problem by adding non-linear and stochastic terms to the usual Schroedinger dynamics. The resulting dynamics localizes in position macroscopic systems, while preserves quantum mechanical predictions for microscopic systems. \nTwo of the main consequences of this resulting dynamics are: the loss of any initial spatial coherence, with a decoherence rate which increases with the dimensions of the system (amplification mechanism); and a heating effect induced on the system that, for long times, leads either to a divergent or to a convergent value of the energy, depending on the particular collapse model considered. \nAn interesting class of system to experimentally test collapse models are cold atomic gases. Besides their very low temperatures (T = 10^(-11) - 10^(-7)K), cold atomic gases show mesoscopic quantum properties, i.e. involving a number of atoms of order of N = 10^(3)– 10^(11). These are all necessary ingredients to experimentally test collapse models. In this thesis, we use cold bosonic atomic gas to test one of the most studied and complete among collapse models, i.e. CSL, and also its non-Markovian and dissipative extensions. In particular, in this thesis we put bounds on CSL free-parameters by studying the diffusion effect induced by collapse noise on a free expanding gas, and we compare the theoretical results with experimental data known in literature. The bounds we put are among the strongest ever found non only for CSL model, but especially for its non-Markovian extension. \nIn this thesis we also specialize the CSL dynamics in Bose-Josephson junctions, and we focus on the localization mechanism induced by the noise on initially entangled states. In particular, we focus on decoherence induced by CSL on typical entangled states as atomic coherent states and NOON states. We find that in the latter ones, CSL effects become significant when the NOON state is composed by a number of atoms of 10^(4) or greater. Moreover, we compare CSL decoherence with environmental decoherence induced by typical realistic sources, as an external thermal cloud, imperfections in the trapping laser, and three body effects. We then find which conditions experiments must fulfill in order to test CSL in a Bose-Josephson junction in conditions never
Abstract This book describes one approach to resolving the ‘measurement problem’ of standard quantum theory (SQT), by changing the Schrodinger equation’s evolution of the wave function. The wave function of SQT does not describe reality. For example, the wave function corresponding to a completed experiment is the sum of terms describing the different experimental outcomes whereas one of these outcomes is what appears in Nature, The rules of SQT respond to this deficiency by imposing an ill-defined ‘collapse postulate.’ The prior smooth evolution of the wave function according to Schrodinger’s equation is replaced by an abrupt ‘jump’ to one of the outcomes. When, why, how are unanswered questions. I have added a term to Schrodinger’s equation, obtaining a theory (which I named the ‘Continuous Spontaneous Localization’ theory, or CSL) that answers these questions. The term has a random field in it: each field makes the sum of terms evolve to one of the terms. The collection of all possible fields produces the (Born rule) probabilistic predictions of SQT. Thus, CSL does something SQT does not: it describes the occurrence of events. But, it is a different theory than SQT, so it predicts different results for some carefully crafted experiments. CSL has now existed for over three decades. While no experiment as yet has proven CSL true, no experiment has conflicted with it either. In this book I have aimed to give a clear exposition of CSL and its consequences, accessible to anyone who has studied SQT.