Non interferometric Tests of the Quantum Superposition Principle
Quantum superpositions lie at the core of quantum mechanics, they are omnipresent in any quantum system and apply to all degrees of freedom. Spatial quantum superpositions are usually studied by interferometric experiments. Interference patterns have been observed for photons and also for massive particles up to the mass of 104 amu. It is still an open question if mesoscopic and even macroscopic objects can in principle be observed in such spatial superpositions.
Interferometric experiments with massive objects are notoriously difficult. The purpose of this discussion meeting is to bring together experts from experimental and theoretical research to explore alternative non-interfrometric experiments, to test the quantum superposition principle in the mesoscopic domain, and at the same time to test alternative models, which explicitly predict a violation of quantum linearity.
Organisers:
Angelo Bassi (University of Trieste)
Hendrik Ulbricht (University of Southampton)
Thursday 17th September:
12:00 – Lunch (Principe di Metternich)
Session 1. Collapse models and proposals for optomechanical tests
Chairman: A. Bassi
14:00 – 14:30 M. Paternostro (Macroscopicity and Collapse in Optomechanics)
14:30 – 15:00 A. Smirne (Dissipative extension of the Continuous Spontaneous Localization (CSL) model)
15:00 – 15:30 S. Nimmrichter (Mass scaling of the CSL diffusion rate in optomechanical experiments)
15:30 – 16:30 Discussion
Session 2. Status of experiments
Chairman: H. Ulbricht
16:30 – 17:00 P. Barker (Cavity cooling of a single charged levitated particle in a Paul trap)
17:00 – 17:30 A. Vinante (Testing collapse models with ultracold mechanical resonators)
17:30 – 18:00 M. Drewsen (Rotational Cooling of Coulomb-Crystallized Molecular Ions by a Helium Buffer Gas)
18:00 – 19:00 Discussion
20:00 – Lunch (Principe di Metternich)
Friday 18th September:
08:15 – Breakfast (Principe di Metternich)
Session 3. Collapse models and proposals for optomechanical tests
Chairman: K. Hornberger
09:00 – 09:30 K. Hammerer (Continuous measurement of optomechanical systems)
09:30 – 10:00 D. Goldwater (Testing Collapse Theories Using Parametric Heating of a Trapped Nanosphere)
10:00 – 10:30 J. Li (Detecting Spontaneous Wave-Function Collapse with Entangled Mechanical Nanoresonators)
10:30 – 11:00 Discussion
Session 4. Status of experiments
Chairman: F. Marino
11:00 – 11:30 R. Riedinger (Position sensing beyond the standard quantum limit)
11:30 – 12:00 F. Marin (Creating squeezed states by parametric excitation)
12:00 – 12:30 C. Curceanu (Spontaneously emitted radiation as a test of the collapse models. Where do we stand?)
12:30 – 13:00 Discussion and closing
13:00 – Lunch (Principe di Metternich)
Extended Program with Abstracts
Thursday 17th September:
12:00 Lunch
Session 1. Collapse models and proposals for optomechanical tests
Chairman: A. Bassi
14:00 – 14:30 M. Paternostro Macroscopicity and Collapse in Optomechanics
I will provide an overview of recent progress made along the lines of shaping an optomechanical route towards the study of fundamental questions verging towards the definition of a proper measure of macroscopic quantumness and the study of collapse models, addressing both the CSL and Newton-Schroedinger models.
14:30 – 15:00 A. Smirne Dissipative extension of the Continuous Spontaneous Localization (CSL) model
Collapse models explain the absence of quantum superpositions at the macroscopic scale, while giving practically the same predictions as quantum mechanics for microscopic systems [1,2,3]. The Continuous Spontaneous Localization (CSL) model is the most refined and studied among collapse
models. A well-known problem of this model, and of similar ones, is the steady and unlimited increase of the energy induced by the collapse noise. In this talk, I discuss the recently introduced dissipative extension of the CSL model [4], which guarantees a finite energy during the entire system’s evolution, thus making a crucial step toward a realistic energy-conserving collapse model. This is achieved by introducing a non-linear stochastic modification of the Schrödinger equation, which represents the action of a dissipative finite-temperature collapse noise. The possibility to introduce dissipation within collapse models in a consistent way will have relevant impact on the experimental investigations of the CSL model [5,6], and therefore also on the testability of the quantum superposition principle.
[1] A. Bassi, K. Lochan, S. Satin, T.P. Singh, and H. Ulbricht, Rev. Mod. Phys. 85, 471 (2013)
[2] G.C. Ghirardi, A. Rimini, and T. Weber, Phys. Rev. D 34, 470 (1986)
[3] G.C. Ghirardi, P. Pearle, and A. Rimini, Phys. Rev. A 42, 78 (1990)
[4] A. Smirne and A. Bassi, Sci. Rep. 5, 12518 (2015)
[5] M. Bahrami, M. Paternostro, A. Bassi, and H. Ulbricht, Phys. Rev. Lett. 112, 210404 (2014)
[6] S. Nimmrichter, K. Hornberger, and K. Hammerer, Phys. Rev. Lett. 113, 020405 (2014)
models. A well-known problem of this model, and of similar ones, is the steady and unlimited increase of the energy induced by the collapse noise. In this talk, I discuss the recently introduced dissipative extension of the CSL model [4], which guarantees a finite energy during the entire system’s evolution, thus making a crucial step toward a realistic energy-conserving collapse model. This is achieved by introducing a non-linear stochastic modification of the Schrödinger equation, which represents the action of a dissipative finite-temperature collapse noise. The possibility to introduce dissipation within collapse models in a consistent way will have relevant impact on the experimental investigations of the CSL model [5,6], and therefore also on the testability of the quantum superposition principle.
[1] A. Bassi, K. Lochan, S. Satin, T.P. Singh, and H. Ulbricht, Rev. Mod. Phys. 85, 471 (2013)
[2] G.C. Ghirardi, A. Rimini, and T. Weber, Phys. Rev. D 34, 470 (1986)
[3] G.C. Ghirardi, P. Pearle, and A. Rimini, Phys. Rev. A 42, 78 (1990)
[4] A. Smirne and A. Bassi, Sci. Rep. 5, 12518 (2015)
[5] M. Bahrami, M. Paternostro, A. Bassi, and H. Ulbricht, Phys. Rev. Lett. 112, 210404 (2014)
[6] S. Nimmrichter, K. Hornberger, and K. Hammerer, Phys. Rev. Lett. 113, 020405 (2014)
15:00 – 15:30 S. Nimmrichter Mass scaling of the CSL diffusion rate in optomechanical experiments
We discuss how the collapse-induced noise in optomechanical experiments depends on the mass and the geometry of the mechanical oscillator. In particular, the noise due to continuous spontaneous localization (CSL) grows sub-linearly with mass, and will therefore be dominated by conventional noise in the limit of large masses.
15:30 – 16:30 Discussion
Session 2. Status of experiments
Chairman: H. Ulbricht
16:30 – 17:00 P. Barker Cavity cooling of a single charged levitated particle in a Paul trap
The cooling of the centre-of-mass motion of a levitated macroscopic particle is seen as an important step towards the creation of long-lived macroscopic quantum states and the study of quantum mechanics and nonclassicality at large mass scales. Levitation in vacuum minimizes coupling to the environment while the lack of clamping leads to extremely high mechanical quality factors of the oscillating particle. The ability to rapidly turn off the levitation coupled with cooling, offers the prospect of interferometry in the absence of any perturbations other than gravity. However, like cold atoms trapped in vacuum, levitated nanoparticles are sensitive to parametric noise and internal heating via even a small absorption of the levitating light field. To date this has limited the lower pressure at which particles can be stably trapped and cavity cooled. We overcome this problem by levitating a naturally charged silica nanosphere in a hybrid electro-optical trap by combining a Paul trap with an optical dipole trap formed from a single mode optical cavity. We show that the hybrid nature of the trap introduces an unexpected synergy where the Paul trap plays an important role in the cavity cooling dynamics by introducing a cyclic displacement of the equilibrium point of the mechanical oscillations in the optical field. This eliminates the need for a second, dedicated cooling optical mode of the cavity and importantly allows us to cool the trapped particle in vacuum to mK temperatures.
17:00 – 17:30 A. Vinante Testing collapse models with ultracold mechanical resonators
A known side effect of collapse models is a slow increase of energy of an isolated system. Several recent proposals (for instance S.Nimmrichter et al Phys. Rev. Lett. 113, 020405; L.Diosi, Phys. Rev. Lett. 114, 050403) suggest that state-of-the-art mechanical resonators of different type could be used to detect this effect and therefore to perform indirect tests of collapse models. The simplest strategy is to accurately measure the mean energy of a cold mechanical resonator in stationary regime, looking for an excess with respect to the expected thermal energy. Here, I will consider nanomechanical resonators cooled to temperatures of a few tens of millikelvin. I will discuss the upper limits on CSL which can be inferred from the data of recent experiments, and from possible refined measurements with improved devices. I will conclude that the full parameter range suggested by Adler, down to a collapse rate <1E-10 Hz, can be in principle tested with existing technology.
17:30 – 18:00 M. Drewsen Rotational Cooling of Coulomb-Crystallized Molecular Ions by a Helium Buffer Gas
In this talk, I will discuss recent experimental results on helium buffer-gas cooling of the rotational degrees of freedom of MgH+ molecular ions, which are trapped and sympathetically crystallized in a linear radio-frequency quadrupole trap [1]. With helium collision rates of only ~10 s^{-1}, i.e. four to five orders of magnitude lower than in usual buffer gas cooling settings, we have cooled a single molecular ion to an unprecedented measured low rotational temperature of 7.5 K. In addition, by only varying the shape and/or the number of atomic and molecular ions in larger Coulomb crystals, we have tuned the effective rotational temperature from ~7 K up to ~60 K by changing the micromotion energy. The very low helium collision rate may potentially even allow for sympathetic sideband cooling of single molecular ions, and eventually make quantum-logic spectroscopy of buffer gas cooled molecular ions feasible. Furthermore, application of the presented cooling scheme to smaller trapped charged nano-particle could potentially be of interest for an initial stage cooling such particles mechanical modes.
[1] Hansen A. K., Versolato O. O., Kłosowski Ł., Kristensen S. B., Gingell A., Schwarz M., Windberger A., Ullrich J., Crespo López-Urrutia J. R. and Drewsen M., Nature 508,76 (2014).
[1] Hansen A. K., Versolato O. O., Kłosowski Ł., Kristensen S. B., Gingell A., Schwarz M., Windberger A., Ullrich J., Crespo López-Urrutia J. R. and Drewsen M., Nature 508,76 (2014).
18:00 – 19:00 Discussion
20:00 – Dinner
Friday 18th September:
Session 3. Collapse models and proposals for optomechanical tests
Chairman: K. Hornberger
09:00 – 09:30 K. Hammerer Continuous measurement of optomechanical systems
I will present non-interferometric tests of macorealistic models which are based on continuous measurements of optomechanical systems. My main point will be to show that at a sufficiently sensitive continuous measurement generates quantum mechanical superposition states which are forbidden by macrorealism.
09:30 – 10:00 D. Goldwater Testing Collapse Theories Using Parametric Heating of a Trapped Nanosphere
We propose a mechanism for testing the theory of continuous spontaneous localization (CSL) by examining the parametric heating rate of a trapped nanosphere. The random localizations of the centre of mass for a given particle predicted by the CSL model can be modelled as a stochastic force embodying a source of heating for the nanosphere. We show that by utilising a Paul trap to levitate the particle coupled with 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 timescale of seconds, and that the full parameter ranges given by Adler [J. Phys. A 40 2935 (2006)] and Bassi [EPL 92 5006 (2010)] ought to be testable using this scheme.
10:00 – 10:30 J. Li Discriminating the effects of collapse models from environmental diffusion with levitated nanospheres
Collapse models postulate the existence of intrinsic noise which modifies quantum mechanics and is responsible for the emergence of macroscopic classicality. Assessing the validity of these models is extremely challenging because, although their expected effects can be significant in various realistic situations, it is nontrivial to discriminate unambiguously their presence in experiments where other hardly controllable sources of noise compete to the overall decoherence. Here we provide a simple procedure able to probe the hypothetical presence of the collapse noise with a levitated nanosphere in a Fabry-Perot cavity. We show that the stationary state of the system is particularly sensitive, under specific experimental conditions, to the interplay between the cavity size, the trapping frequency and the momentum diffusion induced by the collapse models, allowing to detect them even in the presence of standard environmental noises.
10:30 – 11:00 Discussion
Session 4. Status of experiments
Chairman: F. Marino
11:00 – 11:30 R. Riedinger Position sensing beyond the standard quantum limit
Sensing the position of a harmonic oscillator with a continous probe beam is limited by the standard quantum limit. This is the optimum between the uncertainty of the measurement and noise introduced by back action. To resolve smaller quantum features, such as the interference fringes of a Schrödinger Cat state, measurement back action on the observable of interest must be minimized. This can be achieved, e.g. by using instantaneous position measurements. Recent progress in this approach, utilizing optomechanical photonic crystal resonators, is reported.
11:30 – 12:00 F. Marin Creating squeezed states by parametric excitation
We report the experimental observation of single-mode and two-mode squeezing in the oscillation quadratures of a thermal micro-oscillator. These effects are obtained by parametric modulation of the optical spring in a cavity opto-mechanical system. While the present experiments are in the classical regime, in a moderately cooled system our technique can be efficiently exploited to produce strong quantum squeezing and entangled quantum opto-mechanical modes in a macroscopic mechanical oscillator. Such systems would provide an interesting framework for studying effects related to the duration and the possible disappear of peculiar quantum properties.
12:00 – 12:30 C. Curceanu Spontaneously emitted radiation as a test of the collapse models. Where do we stand?
In Quantum Theory we have the “measurement problem”, generated by how (even whether) the wave function describing the system collapses. We do measure a definite state, in spite of the fact that the QT describes a state as (usually) being in a linear superposition of different states. How does the wave function collapse and generates that “event” we measure/see? In the last decades huge theoretical effort was devoted to the development of consistent theoretical models aiming to solve the “measurement problem””. Among these, the Dynamical Reduction Models (DRM) provide a consistent theoretical framework for understanding how “classical world” emerges from quantum mechanics. Their dynamics practically preserves quantum linearity for the microscopic systems, but becomes strongly nonlinear when moving towards macroscopic scale. These types of models can be regarded as effective theories for the “real theory” beyond QT which is yet to be discovered.
The DRM possess the unique characteristic to be experimentally testable, thus enabling to set experimental upper bounds on the reduction rate parameter “lambda” characterizing these models.
The most promising testing ground is offered by the search for the spontaneous radiation emitted by charged particles interacting with the “collapsing field”, which is predicted by the collapse models.
We shall present results coming from a measurement of this spontaneous radiation performed in the low-background underground laboratory of Gran Sasso (LNGS-INFN, Italy) with the aim to put the most stringent limit on the lambda parameter ever and we’ll discuss the results and future perspectives.
The DRM possess the unique characteristic to be experimentally testable, thus enabling to set experimental upper bounds on the reduction rate parameter “lambda” characterizing these models.
The most promising testing ground is offered by the search for the spontaneous radiation emitted by charged particles interacting with the “collapsing field”, which is predicted by the collapse models.
We shall present results coming from a measurement of this spontaneous radiation performed in the low-background underground laboratory of Gran Sasso (LNGS-INFN, Italy) with the aim to put the most stringent limit on the lambda parameter ever and we’ll discuss the results and future perspectives.
12:30 – 13:00 Discussion and closing
13:00 Lunch
Location:
The meeting will take place at The Abdus Salam International Center for Theoretical Physics (ICTP). The meeting room is the Lundqvist Lecture Hall located in the Adriatico Guesthouse of the ICTP. Accommodation will be provided in the Adriatico guesthouse.
Transportation:
Trieste is easily reachable by plane, train and automobile. Arriving by plane, one can choose to land at Ronchi dei Legionari airport, Venice Marco Polo Airport, or Treviso Airport. Trains operated by Trenitalia travel frequently between Trieste and major Italian cities. Buses are available for local and regional transport.
Airport transit:
Trieste is served by the Ronchi dei Legionari Airport the closest and most convenient airport to the city. Visitors can reach the ICTP campus either using Bus Line 51 (Airport Bus 51) or a taxi.
- From airport to ICTP by bus: The bus stops are outside the airport terminal building, on the left. Bus 51 runs from the airport to downtown Trieste and has a stop at Grignano (pronounced greenah’no) close to the ICTP campus and the Adriatico Guesthouse. The Adriatico Guesthouse is downhill from the bus stop and the other buildings are uphill. To reach the guesthouse, turn right down the small road “Via Junker”; the road eventually turns into a series of steps leading to the water’s edge. The Adriatico Guesthouse is on the right. Check the campus map for exact directions. At the airport, bus tickets can be purchased at the Agenzia Turismo FVG on the ground floor or from the automatic machine at the arrivals hall. The cost of bus tickets is around 4 Eur, and have to be purchased before getting on the bus.
Airport Bus E51 Schedule (from Ronchi dei Legionari airport)
- From airport to ICTP by taxi: Taxis can be hailed outside the airport. To reach the Adriatico Guesthouse, provide the address: Via Grignano 9, Trieste; to reach the Galileo Guesthouse: Via Beirut 7, Trieste; to reach the Leonardo Da Vinci Building: Main Building, Strada Costiera 11, Trieste. The cost of a taxi from Ronchi Airport to the ICTP is around Eur 70, plus a small surcharge for each piece of luggage. The cost from Trieste Air Terminal (near central railway station) to the ICTP is approx. Eur 15. Please note that if, at the end of stay, a taxi is hired from a Guest House to the airport, the meter usually starts in Trieste city (from where the taxi is called) and stops at the airport. Thus, the cost is somewhat higher than the incoming journey.
From Venice Marco Polo airport: Visitors can reach ICTP from Venice Marco Polo airport by bus + train (look at the Trenitalia Website for train schedules). The Mestre-Venezia airport buses take approximately half an hour from the airport to the train station Venezia Mestre, where passengers switch to trains that run direct to Trieste. Train tickets must be validated at the validating machines before boarding trains; fines for carrying non-validated tickets are high.
Visitors can reach the ICTP from Venice airport also by using the Science Bus, a private service which connects Trieste with the nearby airports. The shuttle has to be booked in advance. The cost from Venice to Trieste is approximately 190 Eur one way, and it takes 1.5 hours to reach the city, depending on traffic.
Train service:
Italy’s national train service, Trenitalia, operates frequent services between Trieste and several major cities in Italy. Visitors to ICTP can take the train until its endpoint (Trieste Central Station).
For schedule information, please visit the Trenitalia website.
To reach ICTP from the train station, take the local bus no. 6 (see direction here below). Another transport option from Trieste Central Station to ICTP is to take a taxi. Taxis can be hailed from outside the station. Each piece of luggage is charged and taxi fares are higher at night and on holidays.
Local buses:
Local Bus 6 brings visitors to ICTP from Trieste. Tickets for the bus must be purchased before you board the vehicle; you can purchase these at ICTP’s InfoPoint and at the Centre’s guesthouse receptions, as well as at the main train station in Trieste and at many local news vendors.
When coming to Trieste by train, exit the train station on the left right at the end of the tracks. Cross the street and walk some 50 meters to the right. There is a bus stop, where n. 6 stops on the way to Miramare and Grignano. Tickets have to be purchased before getting on the bus. Ask the driver to stop you by the “Center for Theoretical Physics” (“Fisica Teorica” in Italian), which is after some 20 minutes ride. When exiting, stay on the same side of the street and walk for some 50 meters along the direction of the bus. Then turn right in the ICTP campus.
Trieste Bus 6 (from Trieste)
Road directions:
Take the A4 motorway from Venice-Mestre, or the A23 motorway from Tarvisio- Austria. Follow signs for Sistiana-Strada Costiera, then take route SS 14, a panoramic road leading directly to the city centre. The ICTP Campus – Grignano/Miramare area – is about 15 km from the motorway at Strada Costiere, 11.
Participants:
Mohammad Bahrami (University of Trieste – Italy)
Peter Barker (University College London – UK)
Catalina Curceanu (INFN – Frascati – Italy)
Michael Drewsen (Aarhus University – Denmark)
Daniel Goldwater (Imperial College London – UK)
Klemens Hammerer (Albert-Einstein Institute for gravitational physics, Hannover – Germany)
Klaus Hornberger (University of Duisburg-Essen – Germany)
Jie Li (University of Camerino – Italy)
Francesco Marino (CNR-INO Florence – Italy)
Francesco Marin (LENS Florence – Italy)
Stefan Nimmrichter (University of Duisburg-Essen – Germany)
Mauro Paternostro (Queen’s University Belfast – UK)
Ralf Riedinger (University of Vienna – Austria)
Andrea Smirne (University of Ulm – Germany)
Andrea Trombettoni (SISSA – Italy)
Andrea Vinante (INFN Trento – Italy)
Contact: noninterferometric@gmail.com
Sponsored:
Sponsored by INFN Trieste and The John Templeton Foundation
