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My research interests include quantum information science and condensed matter physics. I have made contribution to various areas. Below, I elaborate on specific research directions and highlight some research findings.

I. Quantum Information Processing and Quantum Computation

A. Universal Quantum Computation, Resource States, and Quantum Computational Complexity

Quantum computers are shown in principle to be capable of efficiently solving some problems that are very hard for current computers, even supercomputers. But how can quantum computers be built? There are a few architectures, and among them is the so-called measurement-based model of quantum computation. In this approach, a highly entangled state is used as a resource and subsequent local measurements alone can drive quantum computation. Central questions include (i) What states can actually be used as resources and what are the essential properties? (ii) Can they arise as a unique ground state of physically reasonable model with nice features such as an energy gap?

For example, I uncovered a surprising link between quantum computation and condensed-matter physics:  a family of quantum spin models (called AKLT models) can give rise to resource states that can be used to build measurement-based quantum computers [2,4,6,9,11,14]. This prompted many subsequent studies by other researchers in generalizing our methods in other spin systems and in searching for physical systems to realize these resource states. For example, Bartlett and co-workers extended our methods to the deformed AKLT models and show that there is a region that the deformed AKLT can also be used for universal quantum computation. A few of the AKLT models were believed to possess an energy gap above their ground states, but no proof exists. My collaborators and I managed to compute these gaps and showed them to be finite and nonzero even for system sizes approaching to infinity [10]. Moreover, I discovered that measurement-based quantum computation needs not be performed at zero temperature, it can be carried out at a relatively high temperature, which is important because absolute zero temperature cannot be reached in practice [3]. Extending from that I also demonstrated that there is a new kind of phase transitions defined by the computational power [12].

A recent interest is to search for symmetry-protected topologically ordered states for measurement-based quantum computation. These are short-ranged entangled states that might potentially provide deeper understanding and breakthrough in characterizing resource states[13,60]. 

Quantum computers are powerful, but there can exist problems that even quantum computers cannot efficiently solve. Problems that involve fermions are usually believed to be hard, due to the famous sign problem due to the exchange of these fermionic particles. Conventional wisdom holds that on the contrary bosons, which are sign-free under exchange, are easy. My work overthrows this wisdom and shows that bosonic systems can also pose difficult problems [1]. This prompts further research endeavor of other scientists to work on computational complexity of boson problems and how to improve the current numerical methods dealing with bosons.

My publications in this category include:

[1] "Interacting boson problems can be QMA-hard", T.-C. Wei, M. Mosca, and A. Nayak,
       Phys. Rev. Lett. 104, 040501 (2010)

[2] "Affleck-Kennedy-Lieb-Tasaki State on a Honeycomb Lattice is a Universal Quantum Computational Resource",
      T.-C. Wei, I. Affleck, and R. Raussendorf,  Phys. Rev. Lett. 106, 070501 (2011)  (selected as PRL Editors'
      Suggestion) [cited 83 times ]

[3]  "Thermal State as Universal Resources for Quantum Computation with Always-on Interactions",  Y. Li, D. E.
       Browne, L. C. Kwek, R. Raussendorf, and T.-C. Wei, Phys. Rev. Lett. 107, 060501 (2011) [cited 36 times]

[4] "Quantum computational universality of the Cai-Miyake-Dur-Briegel 2D quantum state from Affleck-Kennedy-
        Lieb-Tasaki quasichains",  T.-C. Wei, R. Raussendorf, and L. C. Kwek, Phys. Rev. A 84, 042333 (2011)

[5] "Symmetry constraints on temporal order in measurement-based quantum computation", R. Raussendorf,
        P. Sarvepalli, T.-C. Wei, and P. Haghnegahdar, Electronic Proceedings in Theoretical Computer Science (EPTCS) 95, pp.219-250 (2012).

[6] "Two-dimensional Affleck-Kennedy-Lieb-Tasaki state on the honeycomb lattice is a universal resource for quantum computation", T.-C. Wei, I. Affleck, and R. Raussendorf, Phys. Rev. A 86, 032328 (2012)

[7] "Quantum computation by measurement", R. Raussendorf and T.-C. Wei, Annual Review of Condensed Matter Physics vol.3, pp.239-261 (2012)

[8]  "Monogamy of entanglement, N-representability problems and ground states", T.-C. Wei,
       International Journal of Modern Physics B 26, 1243014 (2012)

[9] "Quantum computational universality of spin-3/2 Affleck-Kennedy-Lieb-Tasaki states beyond the honeycomb lattice", Tzu-Chieh Wei, Phys. Rev. A 88, 062307 (2013).
 
[10] "Spectral gaps of AKLT Hamiltonians using Tensor Network methods", A. Garcia-Saez, V. Murg, and
       T.-C. Wei, Phys. Rev. B 88, 245118 (2013)

[11] "Hybrid valence-bond states for universal quantum computation",
       Tzu-Chieh Wei, Poya Haghnegahdar, Robert Raussendorf, Phys. Rev. A 90, 042333 (2014)

[12] "Transitions in the quantum computational power",
       Tzu-Chieh Wei, Ying Li and Leong Chuan Kwek, Phys. Rev. A 89, 052315 (2014)

[13] "Ground-state forms of 1D symmetry-protected topological phases and their utility as resource states for
       measurement-based quantum computation",                                      
       Abhishodh Prakash and Tzu-Chieh Wei, Phys. Rev. A 92, 022310 (2015)

[14] "Universal measurement-based quantum computation with spin-2 Affleck-Kennedy-Lieb-Tasaki states",
       Tzu-Chieh Wei and Robert Raussendorf, Phys. Rev A 92, 012310 (2015)

[60] "Symmetry-protected topologically ordered states for universal quantum computation",
       Hendrik Poulsen Nautrup and Tzu-Chieh Wei, Phys. Rev. A 92, 052309 (2015) arXiv:1509.02947

[61] “Hamiltonian quantum computer in one dimension”, Tzu-Chieh Wei and John C. Liang

 B. Entanglement theory and applications to quantum phase transitions and topological orders

Entanglement is what Schrodinger called “a characteristic trait of quantum mechanics”, and it appears ubiquitously in many fields of physics involving quantum many-body systems. How to characterize it properly remains an important issue. I have contributed significantly to the development of the so-called geometric measure of entanglement [15], and have used it and other related approaches to investigate quantum phase transitions [20,24,28,29,30,31] and topological orders [32,33,34,35]. I also showed how this quantity is related to other entanglement measures, and such connection was exploited by other researchers in their work. My paper [15] has since been cited over 250 times in scientific journals and over 410 times according to Google Scholar by physicists, chemists, mathematicians and engineers. This entanglement measure provides a useful alternative to what is called the entanglement entropy, and also gives a very good characterization of the so-called topological entanglement and transitions of topological phases. Our entanglement measure was also used by other researchers to characterize whether quantum states can be used for quantum computational purposes. As seen below, I have contributed extensively to this area of research.

 In addition, I have also identified connections of our entanglement measure to other important measures, and thereby enabled the knowledge of these other quantities of interest [19,21,27]. I also studied general theory of entanglement, which also led to clarification of several issues, such as the how maximal entanglement should be characterized and how it would depend on the measures used as well as how much entanglement can exotic bound entangled states possess [16,17,18,22,23,25,26].

My publications in this category include:

[15] "Geometric measure of entanglement for bipartite and multipartite quantum states",
        T.-C. Wei and P.M. Goldbart, Phys. Rev. A 68, 042307 (2003) [cited over 410 times]

[16] "Maximal entanglement versus entropy for mixed quantum states", T.-C. Wei, K.  Nemoto, P.M. Goldbart,
       P.G. Kwiat, W.J. Munro, and F. Verstraete, Phys. Rev A 67, 022110 (2003) [cited over 260 times]

[17] "Measures of entanglement in bound entangled states", T.-C. Wei, J.B. Altepeter,
        P.M. Goldbart, and W.J. Munro, Phys. Rev. A 70, 022322 (2004) [cited over 33 times]

[18] "Mixed state sensitivity of several quantum information benchmarks", N. A. Peters, T.-C. Wei, and P.G. Kwiat, 
          Phys. Rev. A 70, 052309 (2004)

[19] "Connections between relative entropy of entanglement and geometric measure of entanglement",
         T.-C. Wei, M. Ericsson, P.M. Goldbart, and W. J. Munro, Quantum Info. Comput. v4, p.252-272 (2004)
         [cited over 80 times]

[20] "Global entanglement and quantum criticality in spin chains", T.-C. Wei, D. Das, S. Mukhopadyay,
        S. Vishveshwara, and P.M. Goldbart, Phys. Rev. A 71, 060305(R) (2005) [cited over 90 times]

[21] "Relative entropy of entanglement for multipartite mixed states: Permutation-invariant states and Dur states",
         T.-C. Wei, Phys. Rev. A 78, 012327 (2008) [cited 30 times]

[22] "Maximally entangled three-qubit states via geometric measure of entanglement", S. Tamaryan,
         T.-C. Wei, and D. Park, Phys. Rev. A 80, 052315 (2009) [cited 36 times]

[23] "Geometric measure of entanglement for symmetric states", R. Huebener, M. Kleinmann,
         T.-C. Wei, C. Gonzalez-Guillen, and O. Guehne, Phys. Rev. A 80, 032324 (2009) [cited 68 times]

[24] "Entanglement under the renormalization-group transformations on quantum states and quantum phase
          transitions using matrix product states", T.-C. Wei, Phys. Rev. A 81, 062313 (2010)

[25] "Exchange symmetry and global entanglement and full separability", T.-C. Wei, Phys. Rev. A 81, 054102 (2010)

[26] "Matrix Permanent and Quantum Entanglement of Permutation Invariant States",  T.-C. Wei and S. Severini,
         J. Math. Phys. 51, 092203 (2010)

[27] "Connections of geometric measure of entanglement of pure symmetric states to quantum state estimation",
        L. Chen, H. Zhu, T.-C. Wei, Phys. Rev. A 83, 012305 (2011)

[28] "Phase diagram of the SO(n) bilinear-biquadratic chain from many-body entanglement", R. Orus,
         T.-C. Wei, and H.-H. Tu, Phys. Rev. B 84, 064409 (2011)

[29] "Geometric entanglement of one-dimensional systems: bounds and scalings in the thermodynamic limit",
        R. Orus and T.-C. Wei, Quantum Inf. Comput. 11, 0563-0573 (2011)

[30] "Global geometric entanglement in transverse-field XY spin chains: finite and infinite systems",
        T.-C. Wei, S. Vishveshwara and P.M. Goldbart, Quantum Inf. Comput. 11, 0326 (2011)

[31] "Visualizing elusive phase transitions with geometric entanglement", R. Orus and T.-C. Wei, 
          Phys. Rev. B 81, 155120 (2010)

[32] "Geometric entanglement in topologically ordered states",
        Roman Orus, Tzu-Chieh Wei, Oliver Buerschaper, and Maarten Van den Nest
        New J. Phys. 16, 013015 (2014)

[33] "Topological Minimally Entangled States via Geometric Measure",
       Oliver Buerschaper, Artur García-Saez, Román Orús, and Tzu-Chieh Wei, J. Stat. Mech. (2014) P11009

[34] "Topological Transitions from Multipartite Entanglement with Tensor Networks: A Procedure for Sharper and  
        Faster Characterization", Roman Orus, Tzu-Chieh Wei, Oliver Buerschaper, Artur Garcia-Saez,
        Phys. Rev. Lett. 113, 257202 (2014)

[35] "Transition of a Z3 topologically ordered phase to trivial and critical phases",
       Ching-Yu Huang and Tzu-Chieh Wei, Phys. Rev. B 92, 085405 (2015)

C. Small-scale Physical Implementations of Quantum Simulations and Milestone Experiments

Progress on quantum information has been prompted by implementation of gedanken and proof-of-principle experiments. Before a real full-blown quantum information processing device such as quantum computer can be built, it is vital that fundamental ideas and new information processing methods can be tested in small-scale device. I have contributed significantly to this direction of research and have worked closely with experimentalists to propose feasible small-scale experiments to demonstrate quantum information processing and quantum simulations. Some have been recognized as milestone experiments as evidenced by the number of times our works have been cited by other researchers. These works build foundation of future quantum information technology. For example, we were among the first to demonstrate the use of ancilla to achieve quantum process tomography (even without entanglement) [36]. I helped to solve the problem of how to generate arbitrary two-qubit states [38] and this enabled the realization of creating maximally entangled mixed states and concentrating their entanglement [37]. It is well known in linear optics that the so-called Bell-state analysis cannot be done with 100% success, and given such a limitation, I analyzed and constructed schemes that employs hyperentanglement for transmitting information [40] and such analysis became useful later on and led to subsequent experiments such as the highest channel capacity demonstrated [41]. Recently, I assisted in a collaboration with Kwiat’s team and Herbert Berstein that demonstrates experimentally, for the first time, the utility of the so-called “superdense teleportation” [45].  The analysis that we found is that the superdense teleportation combines the advantage of teleportation and remote state preparation to allow encoding and sending information more efficiently.

My publications in this category include:

[36] "Ancilla-assisted quantum process tomography",  J.B. Altepeter, D. Branning,  
        E. Jeffrey, T.-C. Wei, P.G. Kwiat, R.T. Thew, J.L. O'Brien, M.A. Nielsen,
        and A.G.White, Phys. Rev. Lett. 90, 193601 (2003)
        [cited 217 times]

[37] "Maximally entangled mixed states: creation and concentration",
         N.A. Peters, J.B. Altepeter, D.A. Branning, E.R. Jeffrey, T.-C. Wei, and P.G. Kwiat,
         Phys. Rev.  Lett. 92, 133601 (2004) [cited 103 times]

[38] "Synthesizing arbitrary two-photon polarization mixed states",
        T.-C. Wei, J.B. Altepeter, D. Branning, P.M. Goldbart,  D.F.V. James, E. Jeffrey, P.G. Kwiat, S. Mukhopadhyay,
        and N.A. Peters, Phys. Rev. A 71, 032329 (2005)

[39] "Remote state preparation: arbitrary remote control of photon polarization”,
       N.A. Peters, J. Barreiro, M.E. Goggin, T.-C. Wei, and P.G. Kwiat, Phys. Rev. Lett. 94, 150502 (2005) [cited over
       140 times]

[40] "Hyperentangled Bell-state analysis",
          T.-C. Wei, J.T. Barreiro, and P.G. Kwiat, Phys. Rev. A 75, 060305(R) (2007) [cited 60 times]

[41] "Beating the channel capacity limit for linear photonic superdense coding",
          J.T. Barreiro, T.-C. Wei, and P.G. Kwiat, Nature Phys. 4, 282-286 (2008) [cited 276 times]

[42] "Remote preparation of single-photon "hybrid" entangled and vector-polarization states",
         J.T. Barreiro, T.-C. Wei, and P.G. Kwiat, Phys. Rev. Lett. 105, 030407 (2010) [cited 86 times]

[43]  "Creating multi-photon polarization bound-entangled states",
         T.-C. Wei, J. Lavoie, and R. Kaltenbaek, Phys. Rev. A 83, 033839 (2011)

 [44] "Experimental Quantum Simulation of Entanglement in Many-body
         Systems", J. Zhang, T.-C. Wei, and R. Laflamme,
         Phys. Rev. Lett. 107, 010501 (2011)

 [45] "SuperDense teleportation using hyperentangled photons",
       Trent M. Graham, Herbert J. Bernstein, Tzu-Chieh Wei, Marius Junge, Paul G. Kwiat,
       Nature Communications 6, 7185 (2015)

II. Condensed Matter Physics

My publications in this category include:

      [62]“Detection of gapped phases of a 1D spin chain with onsite and spatial symmetries”,
        Abhishodh Prakash, Colin G. West, Tzu-Chieh Wei, arXiv: 1604.00037 

2.   [63] “Detecting and identifying 2D symmetry-protected topological, symmetry-breaking and intrinsic topological phases with modular matrices via               tensor-network methods”,
        Ching-Yu Huang and Tzu-Chieh Wei, arXiv:1512.07842 (to appear in Physical Review B)

[13] "Ground-state forms of 1D symmetry-protected topological phases and their utility as resource states for
       measurement-based quantum computation",                                      
       Abhishodh Prakash and Tzu-Chieh Wei, Phys. Rev. A 92, 022310 (2015) 

[32] "Geometric entanglement in topologically ordered states",
        Roman Orus, Tzu-Chieh Wei, Oliver Buerschaper, and Maarten Van den Nest
        New J. Phys. 16, 013015 (2014)

[35] "Transition of a Z3 topologically ordered phase to trivial and critical phases",
        Ching-Yu Huang and Tzu-Chieh Wei, Phys. Rev. B 92, 085405 (2015)

B. Application of Tensor Network Methods

The Tensor Network (TN) methods generalize White’s Density Matrix Renormalization Group (DMRG) and provide useful numerical tools for investigating many-body systems beyond one dimension, probing such as the ground state, thermal state, and dynamics. I have utilized some of these methods, such as the matrix product states via the infinite Time Evolving Block Decimation (iTEBD) scheme to obtain approximated ground-state wavefunctions of 1D spin chains and investigate their entanglement properties (see also II.B above) and quantum phase transitions [13,28,31]. In particular, my student and I have examined symmetry-protected topological (SPT) phases with A₄ symmetry and the associated phase diagram using iTEBD and non-local symmetry order parameter [13]. In particular, we found that A₄ SPT symmetry is spontaneously broken down to Z₂xZ₂ SPTO. With collaborators, I have also used the projected entangled pair states (PEPS) to examine the stability of the two-dimensional Z₂ topological phase (as well as Z₃, Z₄ and Z₅ topological phases) under the string tension [34,35]. In [34], we show that the geometric entanglement can provide as an alternative to the entanglement entropy and give a sharper and more efficient characterization of topological entanglement. In [35] we employed the gauge-symmetry preserved tensor renormalization group approach to characterize transitions of, for example, a Z₃ topological phase, making transitions to a trivial product state and a gapless non-topological phase depending on the string tension magnitude. In addition, I have also been working on how the methods of tensor network can be useful for quantities that are usually calculated in other methods such as Monte Carlo, for example, the Binder's cumulant [58]. At the moment, I am exploring how tensor network methods can provide direct probe of the so-called Yang-Lee zeros and Fisher zeros of partition functions, which are very useful in learning about phase transitions [59]. 

My publications in this category include:

[13] "Ground-state forms of 1D symmetry-protected topological phases and their utility as resource states for
       measurement-based quantum computation",                                      
       Abhishodh Prakash and Tzu-Chieh Wei, Phys. Rev. A 92, 022310 (2015)

[28] "Phase diagram of the SO(n) bilinear-biquadratic chain from many-body entanglement", R. Orus,
          T.-C. Wei, and H.-H. Tu, Phys. Rev. B 84, 064409 (2011)

[31] "Visualizing elusive phase transitions with geometric entanglement", R. Orus and T.-C. Wei, 
          Phys. Rev. B 81, 155120 (2010)

[34] "Topological Transitions from Multipartite Entanglement with Tensor Networks: A Procedure for Sharper and  
        Faster Characterization", Roman Orus, Tzu-Chieh Wei, Oliver Buerschaper, Artur Garcia-Saez,
        Phys. Rev. Lett. 113, 257202 (2014)

[35] "Transition of a Z3 topologically ordered phase to trivial and critical phases",
        Ching-Yu Huang and Tzu-Chieh Wei, Phys. Rev. B 92, 085405 (2015)

[58] "Efficient evaluation of high-order moments and cumulants in tensor network states", Colin West, Artur
        Garcia-Saez, and Tzu-Chieh Wei, Phys. Rev. B 92, 115103 (2015)

[59] "Density of Yang-Lee zeros in the thermodynamic limit from tensor network methods", Artur Garcia-Saez
        and Tzu-Chieh Wei, Phys. Rev. B 92, 125132 (2015)

C. Superconductivity in Nanoscale Structure

Motivated by a puzzling data of anomalous critical current vs. magnetic field on superconducting nanowires by an experimental group led by Alexey Berzyradin in University of Illinois, I developed a theory [46] of superconductors with magnetic impurities in the presence of a magnetic field to predict anomalous behavior of superconductivity and successfully explained their data [47]. The fluctuation of switching currents probed at low temperature in their experiments gives rise to a tool to probe thermal and quantum phase slips (that results in electrical resistance), and their subsequent experiments on similar setup (without fields) had shown strong evidence of the so-called quantum phase slips [51]. I also contributed to propose nanowire bridges as a probe of superfluid density and vortex motion in thin superconducting strip and this enabled the experimental study of Miller-Bardeen theory of dirty superconductors and a microscale version of Campbell’s model of field penetration [48]. In addition, I have investigated the fundamental question of small superconducting rings and possible transitions and phase diagram due to the emergence of the single-particle flux quantum [49]. My theory has qualitative and quantitative agreement with the experiments on superconducting hollow cylinders. Furthermore, I have also examined the issue of critical velocity of one-dimensional superconductors [50], and this corrects a mistake in the literature that even appears on a textbook.

My publications in this category include:

[46] "Enhancing superconductivity: Magnetic impurities and their quenching by magnetic fields",
        T.-C. Wei, D. Pekker, A. Rogachev, A. Bezryadin, and P.M. Goldbart,
        Europhys Lett. 75, 943 (2006)

[47] "Magnetic field enhancement of superconductivity in ultra-narrow wires",
        A. Rogachev, T.-C. Wei, D. Pekker, A.T. Bollinger, P. M. Goldbart, A. Bezryadin, 
        Phys. Rev. Lett. 97, 137001 (2006) [cited 61 times]

[48] "Local superfluid densities probed via current-induced superconducting phase gradients",
         D.S. Hopkins, D. Pekker, T.-C. Wei, P.M. Goldbart, and A. Bezryadin,
         Phys. Rev. B 76, 220506 (R) (2007)

[49] "Emergence of h/e-period oscillations in the critical temperature of small superconducting rings threaded by
        magnetic flux", T.-C. Wei and P.M. Goldbart,
        Phys. Rev. B 77, 224512 (2008) [cited 38 times]

[50] "Critical velocity of a clean one-dimensional superconductor",
       T.-C. Wei and P.M. Goldbart, Phys. Rev. B 80, 134507 (2009)

[51]  "Individual topological tunnelling events of a quantum field probed through their macroscopic consequences",
        M. Sahu, M.-H. Bae, A. Rogachev, D. Pekker, T.-C. Wei, N. Shah, P.M. Goldbart and A. Bezryadin,
        Nature Phys. 5, 503 (2009) [cited 62 times]

                                               .                        

D. Field and Strongly-Correlated Effects in Carbon Nanotube and Graphenes

I studied the carbon nanotube, a nano scale cylinder made purely of carbon atoms, with an axial parallel magnetic field. The field enables conversion of a metallic to semiconducting tube continuously and was experimentally probed in Bezryadin’s group of University of Illinois [52].  I was able to help the experimenters to explain their observed phenomena, and their experiment is important because it can be potentially used for improving semiconductor devices. In addition, I investigated the effect of transverse fields (including both electric and magnetic) on metallic, so-called armchair carbon nanotubes. I found a continuous gap opening and breakings of symmetries, such as valley, particle-hole, and left-right-moving degeneracies [53]. The implication of these findings is that by controlling electric or magnetic fields, these nanotubes can be turned from metal to insulator, important for building nano-scale electronic devices.  I also showed how the interaction was modified by fields and how the strongly correlated behavior of electrons was modified and controlled by these fields. In particular, a possible charge-spin-band separation phenomenon can occur [55], and this also has a technological impact if it can be realized in experiments. I also considered gated bilayer graphenes and studied how one-dimensional gapless modes can occur, even with the bulk being gapped, which is of fundamental importance [54].

 My publications in this category include:
 

[52] "h/e magnetic flux modulation of the energy gap in nanotube quantum dots",
     U.C. Coskun, T.-C. Wei, S. Vishveshwara, P.M. Goldbart, and A. Bezryadin,
     Science v.304, p.1132-1134 (2004) [cited 114 times]

[53] "Transverse field-induced effects in carbon nanotubes",
       W. DeGottardi, T.-C. Wei and S. Vishveshwara,
       Phys. Rev. B 79, 205421 (2009)

[54] "Tomonaga-Luttinger liquid physics in gated bilayer graphene",
       M. Killi, T.-C. Wei, I. Affleck, and A. Paramekanti,
       Phys. Rev. Lett. 104, 216406 (2010) [cited over 32 times]

[55]  "Accessing nanotube bands via crossed electric and magnetic fields",
        W. DeGottardi, T.-C. Wei, V. Fernandez, and S. Vishveshwara,
        Phys. Rev. B 82, 155411 (2010)

E. Cold Atoms in Optical Lattice and BEC

I studied Bose gas in optical lattices and accounted for the inhomogeneous superfluid and Mott structures and provided a simple counting recipe for creating the so-called Mott states that may be potentially useful in quantum information processing using cold atoms [55]. Experimental works led by prestigious scientists, Ketterle [Science 313, 649 (2006)] and of Bloch [Phys. Rev. Lett. 95, 050404 (2005)] have achieved observation of the wedding-cake structure using setups similar to our proposals, and both works cited our paper. Furthermore, I investigated collective modes and dynamics of superfluids in novel geometries such as a bubble trap [57]. In particular, the expansion of a shell trap results in self-interference and a seemingly shock wave, and this shows how the Bose-Einstein condensation can be used to produce interesting self-interference effect and simulate shock waves.

My publications in this category include:

[56] "Structure and stability of Mott-insulator shells of bosons trapped in an optical lattice",
        B. DeMarco, C. Lannert, S. Vishveshwara, and T.-C. Wei,
        Phys. Rev. A 71, 063601 (2005) [cited 74 times]

[57] "The dynamics of condensate shells: collective modes and expansion",
       C. Lannert, T.-C. Wei, S. Vishveshwara,
       Phys. Rev. A 75, 013611 (2007)