Pseudo-magnetic forces and fields for atoms and photons


This project is funded by The Unity Through Knowledge Fund (UKF).      


This proposal aims to discover novel schemes for creating pseudo-magnetic fields (also referred to as synthetic magnetic fields) for atoms and photons, and to provide experimental demonstrations of some magnetic effects such as the Lorentz force via these schemes. The targeted systems are ultracold atomic gases (experimental and theoretical effort), and propagating laser beams in photonic structures (theoretical effort, experiments could follow up this project).

The motivation for this study in simple words is as follows. Magnetic fields occur near bar magnets or wires carrying currents. When a charged particle such as electron moves in a magnetic field, it feels a force perpendicular to its velocity. This force is called the Lorentz force, and it is a consequence of the interaction of a charged particle and the magnetic field. However, if an electrically neutral particle such as an atom would move in a magnetic field, it would not feel the Lorentz force as an electron would. Similarly, a light beam passing through such a magnetic field would not feel its presence. Here we want to construct artificial systems, where the behavior of atoms and photons in these artificial systems would be analogous to behavior of electrons in magnetic fields.

We consider ultracold atomic gases and propagating laser beams in photonic structures. These systems have attracted considerable attention in the recent decades. By introducing pseudo-magnetic fields and consequently magnetic effects in those systems would open the way for studies of magnetic phenomena analogous to those in electronic systems, and potentially lead to their applications.

We propose to study and implement, theoretically and experimentally, novel schemes realizing pseudo-magnetic (synthetic magnetic) forces for an ultracold classical gas of neutral atoms. The scheme utilizes resonant interaction of laser beams with internal atomic levels in a Magneto-Optical Trap (MOT), yielding a characteristic Lorentz-like force. Our experiments are performed using 87Rb atomic cloud in the MOT.

Our teams have long-term experience in the fields of optics and photonics, and ultracold atomic gases. We find it synergetic to investigate the possibility of implementing new schemes for creating synthetic magnetic fields acting on laser beams propagating through specially tailored photonic materials.





This project involves three groups that are lead by:

1.      Prof. Hrvoje Buljan, Principal Investigator (PI), Department of Physics, Faculty of Science, University of Zagreb, Bijenička cesta 32, Zagreb, Croatia

2.      Prof. Marin Soljačić, Co-Principal Investigator (Co-PI), Massachusetts Institute of Technology, Cambridge MA 02139, USA

3.      Dr. Ticijana Ban, Senior Scientist at Institute of Physics, Zagreb (leader of the experimental group).

Other team members are:

4.      Neven Šantić (PhD student), Department of Physics, Faculty of Science

5.      Gordana Kregar (PhD student), Institute of Physics

6.      Dr. Dario Jukić (Investigator, postdoc), now at Faculty of Civil Engineering, University of Zagreb

7.      Dr. Nataša Vujičić (Investigator), Institute of Physics

8.    Dr. Damir Aumiler (Investigator), Institute of Physics

9. Robert Pezer (Investigator), Faculty of Metallurgy

10. Karlo Lelas (investigator, postdoc), now at Faculty of Textile Technology11. Nikola Drpić (PhD student), Department of Physics, Faculty of Science




Workshop in Zagreb, Topological effects and synthetic magnetic fields for atoms and photons, see

In the final month of this project, wee have organized a workshop in Zagreb, titled Topological effects and synthetic magnetic fields for atoms and photons, where we gathered about 60 participants from around the world and Croatia, discussed the topics related to the UKF grant, and presented our group in the scientific community. We had 16 invited speakers that are leading scientists in the topics related to our UKF grant. The website of our workshop is




Papers published within this project

1. Tena Dubček, Colin J. Kennedy, Ling Lu, Wolfgang Ketterle, Marin Soljačić, and Hrvoje Buljan, Weyl Points in Three-Dimensional Optical Lattices: Synthetic Magnetic Monopoles in Momentum Space, Phys. Rev. Lett. 114, 225301 (2015) (

Abstract: We show that Hamiltonians with Weyl points can be realized for ultracold atoms using laser-assisted tunneling in three-dimensional optical lattices. Weyl points are synthetic magnetic monopoles that exhibit a robust, three-dimensional linear dispersion. They are associated with many interesting topological states of matter, such as Weyl semimetals and chiral Weyl fermions. However, Weyl points have yet to be experimentally observed in any system. We show that this elusive goal is well-within experimental reach with an extension of the techniques recently used to obtain the Harper Hamiltonian.


2. Šantić, T. Dubček, D. Aumiler, H. Buljan, T. Ban, Experimental Demonstration of a Synthetic Lorentz Force by Using Radiation Pressure, Scientific Reports 5, 13485 (2015) (

Abstract: Synthetic magnetism in cold atomic gases opened the doors to many exciting novel physical systems and phenomena. Ubiquitous are the methods used for the creation of synthetic magnetic fields. They
include rapidly rotating Bose-Einstein condensates employing the analogy between the Coriolis and the Lorentz force, and laser-atom interactions employing the analogy between the Berry phase and
the Aharonov-Bohm phase. Interestingly, radiation pressure - being one of the most common forces induced by light - has not yet been used for synthetic magnetism. We experimentally demonstrate
a synthetic Lorentz force, based on the radiation pressure and the Doppler effect, by observing the centre-of-mass motion of a cold atomic cloud. The force is perpendicular to the velocity of the cold
atomic cloud, and zero for the cloud at rest. Our novel concept is straightforward to implement in a large volume, for a broad range of velocities, and can be extended to different geometries.


3. T. Dubček, N. Šantić, D. Jukić, D. Aumiler, T. Ban, and H. Buljan, Synthetic Lorentz force in classical atomic gases via Doppler effect and radiation pressure, Phys. Rev. A 89, 063415 (2014) (

Abstract: We theoretically predict synthetic Lorentz force for classical (cold) atomic gases, which is based on the Doppler effect and radiation pressure. A fairly spatially uniform and strong force can be constructed for gases in macroscopic volumes of several cubic millimeters and more. This opens the possibility to mimic classical charged gases in magnetic fields in cold-atom experiments.



Figure shows one possible scheme employing 2 different lasers split in 6 beams on 87Rb hyperfine levels to achieve laser-induced force that depends on the atomic velocity just like the Lorentz force acting on a charged particle in magnetic field.

4. Tena Dubček, Karlo Lelas, Dario Jukić, Robert Pezer, Marin Soljačić, Hrvoje Buljan, The Harper-Hofstadter Hamiltonian and conical diffraction in photonic lattices with grating assisted tunneling, accepted for publication in New Journal of Physics

Abstract: We propose the realization of a grating assisted tunneling scheme for tunable synthetic magnetic fields in optically induced one- and two-dimensional dielectric photonic lattices. As a signature of the synthetic magnetic fields, we demonstrate conical diffraction patterns in particular realization of these lattices, which possess Dirac points in k-space.Wecompare the light propagation in these realistic (continuous) systems with the evolution in discrete models representing the Harper–Hofstadter Hamiltonian, and obtain excellent agreement.


5. Jorge Bravo-Abad, Ling Lu, Liang Fu, Hrvoje Buljan and Marin Soljačić, Weyl points in photonic-crystal superlattices, 2D Mater. 2, 034013 (2015) (;

Abstract: We show that Weyl points can be realized in all-dielectric superlattices based on three-dimensional (3D) layered photonic crystals. Our approach is based on creating an inversion-breaking array of weakly-coupled planar defects embedded in a periodic layered structure with a large omnidirectional photonic band gap. Using detailed band structure calculations and tight-binding theory arguments, we demonstrate that this class of layered systems can be tailored to display 3D linear point degeneracies between two photonic bands, without breaking time-reversal symmetry and using a configuration that is readily-accessible experimentally. These results open new prospects for the observation of Weyl points in the near-infrared and optical regimes and for the application of Weyl-physics in integrated photonic devices.


 6. G. Kregar, N. Šantić, D. Aumiler, H. Buljan, and T. Ban Frequency comb induced radiative force on cold Rubidium atoms by, Physical Review A 89, 053421 (2014) (

In this paper we pointed out that previous assumptions about the frequency comb laser force on atoms that are prevalent in the field are now overturned. The measured force of a femtosecond laser on a cold atomic cloud in the out-of-phase counterpropagating configuration intrigues and challenges previous models. A potential reason for the discrepancy is that the boundary between quantum and classical worlds is not sharp but rather something like many shades of grey. The coupling of internal (quantum) and center-of-mass (classical) degrees of freedom, which is ubiquitous in any model calculating the laser force in atomic systems, is shown to be nontrivial here. It could depend on how quantum entanglement between internal and center-of-mass coordinates decays, which should be taken into account when we transfer information from the quantum to the classical world.  Quite surprisingly, we point out that a very simple experimental setup measuring the laser induced force could potentially probe the boundary between quantum and classical, and explore fundamental phenomena such as decoherence.

7. G. Kregar, N. Šantić, D. Aumiler, and T. Ban, Radiation pressure force on cold rubidium atoms due to excitation to a non-cooling hyperfine level, Europ. Phys. J. D 68, 360 (2014) (

Abstract: We study the radiation pressure force exerted on cold 87Rb atoms captured in a magneto-optical trap (MOT) due to resonant excitation of atoms into the non-cooling 5P1 / 2(F e = 2) hyperfine level. We measure the fractional excited population for different MOT parameters such as cooling laser detuning and power, and empirically test the applicability of the Optical Bloch Equations for describing cold atoms in the MOT. We use the effective saturation intensity parameter which enables simple calculation of the fractional excited state population in a multi-level system using a two-level model, and apply it for the radiative force modeling. This approach provides a valuable tool for optical manipulation experiments.


8. M. Jablan, M. Soljačić, and H. Buljan Effects of screening on the optical absorption in graphene and in metallic monolayers, Phys. Rev. B 89 085415 (2014) ( This paper is continuation of our collaboration with Prof. Soljačić.





The goals / what has been achieved in the UKF grant

The main goals of the project Pseudomagnetic forces and fields for atoms and photons were to (i) invent and theoretically explore schemes for creating pseudomagnetic (also referred to as synthetic) magnetic fields for cold atomic gases, and the effects produced by those fields in realistic systems, (ii) upgrade the experimental capabilities and start a new laboratory for investigating synthetic magnetic phenomena in cold atomic gases in Zagreb, (iii) experimentally explore one new scheme developed in Zagreb, and produce synthetic magnetic effects with this scheme in Zagreb, (iv) invent and theoretically explore synthetic magnetic fields and corresponding effects in photonic systems, (v) establish strong links and collaboration between Massachusetts Institute of Technology (MIT) and the Department of Physics, Faculty of Science, University of Zagreb, and the Institute of Physics in Zagreb, (vi) disseminate the results of our newly established Zagreb team in the scientific community by publishing scientific papers, by presenting talks at workshops, conferences and scientific institutions, and finally by organizing a workshop in Zagreb on the topics related to the UKF grant. All of the goals (milestones and key performance indicators) of our project were achieved.

The program that was carried out was conceptually divided in four workpackages, WP1: Coordination and management, WP2: Synthetic Magnetic Forces/Fields (SMF) on ultracold atoms – theory, WP3: SMF on ultracold atoms – experiment, and WP4: SMF in photonic structures – theory. First we outline the main results in the scientific workpackages WP2-4, and in the end results of the management WP1.

WP2. In collaboration with two MIT groups, that of Prof. Marin Soljačić and Prof. Wolfgang Ketterle, we developed an idea on how to experimentally realize the so-called Weyl Hamiltonian with cold atoms by using synthetic magnetism for ultracold atoms. The experimental realization of this Hamiltonian waited from 1929, when the original theoretical paper by Hermann Weyl was published, until 2015 when it was realized in condensed matter systems. We have published our proposal in Physical Review Letters ( Next, we have proposed one experimentally feasible scheme for creating synthetic Lorentz force in classical cold atomic gases, which is based on the Doppler effect and radiation pressure. This is the 1st proposal for creating the synthetic magnetic force in classical atomic gases, which employs laser-atom interactions. This result was published in Physical Review A (

WP3. We experimentally realized the synthetic magnetic force (SMF) in neutral cold 87Rb atoms by following our theoretical proposal from WP2. We have demonstrated the existence of SMF by observing the motion of the center of mass of the cloud of cold atoms that was initially accelerated by moving the center of the Magneto-Optical Trap (MOT) with time dependent magnetic fields. The results were published in Scientific Reports ( from the publishers of Nature. We have also demonstrated that an expanding atomic cloud gains angular momentum (rotates) during expansion in the presence of the synthetic magnetic force. In addition, we have also demonstrated intriguing force of the femto-second laser on cold atoms (, which hold potential to probe the boundary between the quantum and classical world.

WP4. We have used the so-called laser assisted tunneling scheme from ultracold atomic gases in photonics, where it can be implemented in optically induced photonic lattices. We termed this scheme grating assisted tunneling (we discussed its implementation in photorefractive materials). In our work, we demonstrated the conical diffraction pattern in particular realizations of 1D and 2D square photonic lattices as the signature of the realization of the so-called (alpha=1/2) Harper-Hofstadter Hamiltonian (HHH) in these systems. HHH is the paradigmatic Hamiltonian used for electrons in magnetic fields. We have demonstrated the validity of the scheme by using continuous realistic photonic systems, and this paper was accepted for publication in the New Journal of Physics. In addition, we have also published a proposal for realization of the Weyl points in photonic-crystal superlattices in 2D materials journal. In this effort, we have relied on the expertise that we have in the fields of photonics as well as cold gases. Both papers are in collaboration with the MIT group.

WP1. We have procured equipment and installed a new laboratory for cold atomic gases by using UKF funds. We employed two PhD students on the UKF grant, Tena Dubček and Neven Šantić. Both of them are proceeding well towards defending their doctoral dissertation. We have presented our group and the results by presenting talks at workshops and conferences, and at international institutions (including MIT), and in a few media presentations. Finally, we have organized a workshop in Zagreb, titled Topological effects and synthetic magnetic fields for atoms and photons, where we gathered about 60 participants from around the world and Croatia, discussed the topics related to the UKF grant, and presented our group in the scientific community. The website of our workshop is Finally, let us say that the PI of the UKF grant is leading the Center of Excellence for the Theory of Quantum and Complex Systems – QuantiX - that was approved for funding a few weeks after UKF grant completed; some of the ideas proposed in QuantiX were born while working on the UKF grant.




Ciljevi / što je učinjeno na UKF projektu (hrvatska verzija)

Glavni ciljevi koje smo postavili radeći na projektu „Pseudomagnetske sile i polja za atome i fotone“ (Pseudomagnetic forces and fields for atoms and photons) su bili sljedeći: (i) izmisliti i teorijski istražiti sheme za izradu pseudomagnetskih (također se spominju kao sintetička) magnetskih polja za hladne atomske plinove, kao i učinke koje ta polja proizvode u realističnim sustavima, (ii) nadograditi eksperimentalne mogućnosti i započeti s radom novog laboratorija za istraživanje sintetskih magnetskih pojava u hladnim atomskim plinovima u Zagrebu, (iii) eksperimentalno istražiti jednu novu shemu razvijenu u Zagrebu, i proizvesti sintetičke magnetske učinke pomoću te sheme u Zagrebu, (iv) izmisliti i teorijski istražiti sintetička magnetska polja i odgovarajuće učinke u fotoničkim sustavima, (v) uspostaviti čvrste veze i suradnju između Massachusetts Institute of Technology (MIT) i Fizičkog odsjeka, Prirodoslovno-matematičkog fakulteta, Sveučilišta u Zagrebu i Instituta za fiziku u Zagrebu, (vi) upoznati znanstvenu zajednicu s rezultatima našeg novoosnovanog zagrebačkog tima kroz objavljivanje znanstvenih radova, predavanja na radionicama, konferencijama i znanstvenim institucijama, te konačno organiziranjem radionice u Zagrebu o temama vezanim uz UKF potporu. Svi od navedenih postavljenih ciljeva (zadataka i ključnih pokazatelja uspješnosti) našeg projekta su postignuti.

Izvedeni je program konceptualno bio podijeljen na 4 radne cjeline, WP1: Koordinacija i upravljanje, WP2: Sintetske magnetske sile /polja (SMF) na ultrahladnim atomima - teorija, WP3: SMF na ultrahladnim atomima - eksperiment, i WP4: SMF u fotoničkim strukturama - teorija. U ovom sažetku prvo prezentiramo glavne rezultate u pojedinim znanstvenim radnim cjelinama WP2-4, te na kraju rezultate upravljanja u cjelini WP1.

WP2. U suradnji s dvjema grupama s MIT-a, a to su grupe prof. Marina Soljačića i prof. Wolfganga Ketterlea, razvili smo ideju o tome kako eksperimentalno ostvariti tzv. Weylov Hamiltonian s hladnim atomima pomoću sintetičkog magnetizma za ultrahladne atome. Eksperimentalna realizacija ovog Hamiltoniana čekala se od 1929., kada je Hermann Weyl objavio izvoran teorijski rad, do 2015. godine, kada je Weylov Hamiltonian realiziran u sustavima kondenzirane materije. Naš prijedlog bio je objavljen u znanstvenom časopisu Physical Review Letters (

Nadalje, predložili smo jednu eksperimentalno izvedivu shemu za stvaranje sintetske Lorentzove sile u klasičnim hladnim atomskim plinovima, koja se temelji na Dopplerovom učinku i tlaku zračenja. To je ujedno prvi prijedlog za stvaranje sintetičke magnetske sile u klasičnim atomskim plinovima koji se zasniva na međudjelovanju lasera i atoma. Ovaj rezultat je objavljen u znanstvenom časopisu Physical Review A (

WP3. Eksperimentalno smo dokazali postojanje sintičke magnetske sile (SMF) u neutralno hladnim 87Rb atomima slijedeći naš teoretski prijedlog iz WP2. Dokazali smo postojanje SMF promatranjem gibanja centra mase oblaka hladnih atoma. Tje je oblak na početku ubrzan pomicanjem središta magnetsko-optičke zamke (MOT - Magneto-Optical Trap) s vremensko-zavisnim magnetskim poljima. Rezultati su objavljeni u znanstvenom časopisu Scientific Reports od izdavača Nature
Također smo pokazali da atomski oblak koji se širi dobiva zakretni impuls (rotira) tijekom ekspanzije u prisutnosti sintetičke magnetske sile. Nadalje, pokazali smo intrigantnu silu femto-sekundnog lasera na hladnim atoma ( , koji drže potencijal da istraže granicu između kvantnog i klasičnog svijeta.

WP4. Koristili smo tzv. laserski potpomognuto tuneliranje iz ultrahladnih atomskih plinova u fotoničkim sustavima. Tamo se ta shema može implementirati u optički induciranim fotoničkim rešetkama. Nazvali smo ovu shemu tuneliranje potpomognuto rešetkom (razmatrali smo njezinu provedbu/implementaciju u fotorefraktivnim materijalima). U našem radu, pokazali smo konusnu difrakciju u pojedinim ostvarenjima 1D i 2D kvadratnih fotoničkih rešetki kao i dokaz realizacije tzv. (alfa = 1/2) Harper-Hofstadter Hamiltoniana (HHH) u tim sustavima. HHH je paradigmatski Hamiltonian koji se koristi za elektrone u magnetskim poljima. Mi smo dokazali preciznost i izvedivost sheme koristeći kontinuirane realistične fotonske sustave, i taj naš rad je prihvaćen za objavljivanje u časopisu New Journal of Physics. Također smo objavili prijedlog za realizaciju Weylovih točaka u fotoničkim kristalnim super-rešetkama u časopisu o 2D materijalima. U tom smo se radu oslanjali na našu stručnost iz područja fotonike i hladnih atomskih plinova. Oba su rada napravljena u suradnji s MIT grupom.

WP1. Nabavili smo opremu i ustrojili tj. započeli s radom novog laboratorija za hladne atomske plinove pomoću UKF sredstava. Uz pomoć UKF stipendije/sredstava smo zaposlili dva doktoranta, Tenu Dubček i Nevena Šantića. Trenutno oboje uspješno rade na svojim doktorskim disertacijama. Predstavili smo našu grupu i dobivene rezultate održavanjem predavanja na radionicama i konferencijama, te u međunarodnim institucijama (uključujući MIT), kao i u nekoliko medijskih istupa. Konačno, organizirali smo radionicu u Zagrebu pod nazivom „Topološki efekti i sintetička magnetska polja za atome i fotone“ (Topological effects and synthetic magnetic fields for atoms and photons), u kojoj smo okupili oko 60 sudionika iz cijelog svijeta i Hrvatske, te na kojoj su se raspravljale teme povezane s UKF potporom, i predstavila naša skupina znanstvenoj zajednici. Web stranica radionice nalazi se na poveznici Zaključno, vrijedi spomenuti da glavni istraživač na UKF potpori vodi „Centar izvrsnosti za teoriju kvantnih i kompleksnih sustava“ (Center of Excellence for the Theory of Quantum and Complex Systems) - QuantiX - koji je odobren za financiranje nekoliko tjedana nakon završetka UKF potpore; neke od ideja koje su predložene u QuantiX-u su nastale i osmišljene tijekom rada na UKF potpori.