Home Research Interests Teaching Our Group CV Publications My papers on arXiv GoogleScholar

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*",

[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] "

[11] "*Hybrid
valence-bond states for universal quantum computation*",

**Tzu-Chieh Wei**, Poya Haghnegahdar, Robert
Raussendorf, Phys. Rev. A **90**,
042333 (2014)

*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

[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)

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 â€œa
characteristic trait of quantum mechanicsâ€, 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.

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. v 4, 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*",

[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 GarcÃa-Saez,
RomÃ¡n OrÃºs, 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,

Phys. Rev. Lett.

[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 Kwiatâ€™s team and Herbert
Berstein that demonstrates experimentally, for the first time, the utility of
the so-called â€œsuperdense teleportationâ€ [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.

*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*â€,

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)

*Experimental Quantum Simulation of Entanglement in Many-body
Systems*",
J. Zhang,

Phys. Rev. Lett.

*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
**

I recent got interested in topological phases. The intrinsic topological order originated from the study of fractional quantum Hall effect, but was later found to exist in many other places, such as spin liquid, quantum dimer models, toric code /quantum double models, string-net, etc. Their ground-state degeneracy depends on the topology of the underlying manifold, and excitations have nontrivial statistics. There is no local order parameter for topological ordered phases. They can be useful for quantum computation. On the other hand, there is another kind of phase of matter, which is trivial if no symmetry is respected but exhibits nontrivial order (with the nontrivial order possibly classified by cohomology, cobordism, anomaly, etc.). This includes the topological insulators but also other spin models that may not be easily realized. There is much progress on their classification. I am interested in how to characterize them or how to detect them theoretically or numerically if you are given a Hamiltonian. What phases can actually occur? How to find the transitions of these phases to other ones? Can any of these phases be useful for, say, quantum information processing?

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

[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)

Oliver Buerschaper, Artur GarcÃa-Saez, RomÃ¡n OrÃºs, and

[34] "

Faster Characterization

Phys. Rev. Lett.

[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)

Hendrik Poulsen Nautrup and Tzu-Chieh Wei, Phys. Rev. A

**B. Application of
Tensor Network Methods**

The Tensor Network (TN) methods generalize Whiteâ€™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 A_{4} symmetry and the
associated phase diagram using iTEBD and non-local symmetry order parameter
[13]. In particular, we found that A_{4} SPT symmetry is spontaneously
broken down to Z_{2}xZ_{2} SPTO. With collaborators, I have
also used the projected entangled pair states (PEPS) to examine the stability
of the two-dimensional Z_{2} topological phase (as well as Z_{3},
Z_{4} and Z_{5} 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 Z_{3} 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:

*Ground-state forms of 1D symmetry-protected topological phases and
their utility as resource states for
measurement-based quantum
computation*",

Abhishodh Prakash and

[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)

*Visualizing elusive phase transitions with geometric entanglement*",
R. Orus and **T.-C. Wei**,

Phys. Rev. B **81**, 155120
(2010)

*Topological Transitions from Multipartite Entanglement with Tensor
Networks: A Procedure for Sharper and
Faster Characterization*", Roman
Orus,

Phys. Rev. Lett.

[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)

Garcia-Saez, and **Tzu-Chieh Wei**, Phys. Rev. B **92**, 115103 (2015)

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 Campbellâ€™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]

D.S. Hopkins, D. Pekker, T.-C. Wei, P.M. Goldbart, and A. Bezryadin,

[49]
"*Emergence of h/e-period oscillations in
the critical temperature of small superconducting rings threaded by
magnetic flux*",

[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
Bezryadinâ€™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].

[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

__Phys. Rev. B 79, 205421 (2009)__

[54]
"*Tomonaga-Luttinger liquid physics in
gated bilayer graphene*",

M. Killi, **T.-C. Wei**,

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

**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)